Order-infinite-3 triangular honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=240 !bgcolor=#efdcc3 colspan=2|Order-infinite-3 triangular honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{3,∞,3} |- |bgcolor=#efdcc3|Coxeter diagrams|| |- |bgcolor=#efdcc3|Cells||{3,∞} 40px |- |bgcolor=#efdcc3|Faces||{3} |- |bgcolor=#efdcc3|Edge figure||{3} |- |bgcolor=#efdcc3|Vertex figure||{∞,3} 50px |- |bgcolor=#efdcc3|Dual||Self-dual |- |bgcolor=#efdcc3|Coxeter group||[3,∞,3] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-3 triangular honeycomb (or 3,∞,3 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,∞,3}.

Geometry

It has three Infinite-order triangular tiling {3,∞} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many triangular tilings existing around each vertex in an order-3 apeirogonal tiling vertex figure.

{| class=wikitable width=640 |320px
Poincaré disk model |320px
Ideal surface |}

Related polytopes and honeycombs

It is a part of a sequence of regular honeycombs with Infinite-order triangular tiling cells: {3,∞,p}.

It is a part of a sequence of regular honeycombs with order-3 apeirogonal tiling vertex figures: {p,∞,3}.

It is a part of a sequence of self-dual regular honeycombs: {p,∞,p}.

Order-infinite-4 triangular honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=240 !bgcolor=#efdcc3 colspan=2|Order-infinite-4 triangular honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{3,∞,4}
{3,∞^1,1} |- |bgcolor=#efdcc3|Coxeter diagrams||
= |- |bgcolor=#efdcc3|Cells||{3,∞} 40px |- |bgcolor=#efdcc3|Faces||{3} |- |bgcolor=#efdcc3|Edge figure||{4} |- |bgcolor=#efdcc3|Vertex figure||{∞,4} 50px
r{∞,∞} 50px |- |bgcolor=#efdcc3|Dual||{4,∞,3} |- |bgcolor=#efdcc3|Coxeter group||[3,∞,4]
[3,∞^1,1] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-4 triangular honeycomb (or 3,∞,4 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,∞,4}.

It has four infinite-order triangular tilings, {3,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many infinite-order triangular tilings existing around each vertex in an order-4 apeirogonal tiling vertex figure.

{| class=wikitable width=480 |240px
Poincaré disk model |240px
Ideal surface |}

It has a second construction as a uniform honeycomb, Schläfli symbol {3,∞^1,1}, Coxeter diagram, , with alternating types or colors of infinite-order triangular tiling cells. In Coxeter notation the half symmetry is [3,∞,4,1⁺] = [3,∞^1,1].

Order-infinite-5 triangular honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=280 !bgcolor=#efdcc3 colspan=2|Order-infinite-5 triangular honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{3,∞,5} |- |bgcolor=#efdcc3|Coxeter diagrams|| |- |bgcolor=#efdcc3|Cells||{3,∞} 40px |- |bgcolor=#efdcc3|Faces||{3} |- |bgcolor=#efdcc3|Edge figure||{5} |- |bgcolor=#efdcc3|Vertex figure||{∞,5} 40px |- |bgcolor=#efdcc3|Dual||{5,∞,3} |- |bgcolor=#efdcc3|Coxeter group||[3,∞,5] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-3 triangular honeycomb (or 3,∞,5 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,∞,5}. It has five infinite-order triangular tiling, {3,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many infinite-order triangular tilings existing around each vertex in an order-5 apeirogonal tiling vertex figure.

{| class=wikitable width=480 |240px
Poincaré disk model |240px
Ideal surface |}

Order-infinite-6 triangular honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=240 !bgcolor=#efdcc3 colspan=2|Order-infinite-6 triangular honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{3,∞,6}
{3,(∞,3,∞)} |- |bgcolor=#efdcc3|Coxeter diagrams||
= |- |bgcolor=#efdcc3|Cells||{3,∞} 40px |- |bgcolor=#efdcc3|Faces||{3} |- |bgcolor=#efdcc3|Edge figure||{6} |- |bgcolor=#efdcc3|Vertex figure||{∞,6} 40px
{(∞,3,∞)} 40px |- |bgcolor=#efdcc3|Dual||{6,∞,3} |- |bgcolor=#efdcc3|Coxeter group||[3,∞,6] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-6 triangular honeycomb (or 3,∞,6 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,∞,6}. It has infinitely many infinite-order triangular tiling, {3,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many infinite-order triangular tilings existing around each vertex in an order-6 apeirogonal tiling, {∞,6}, vertex figure.

{| class=wikitable width=480 |240px
Poincaré disk model |240px
Ideal surface |}

Order-infinite-7 triangular honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=240 !bgcolor=#efdcc3 colspan=2|Order-infinite-7 triangular honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{3,∞,7} |- |bgcolor=#efdcc3|Coxeter diagrams|| |- |bgcolor=#efdcc3|Cells||{3,∞} 40px |- |bgcolor=#efdcc3|Faces||{3} |- |bgcolor=#efdcc3|Edge figure||{7} |- |bgcolor=#efdcc3|Vertex figure||{∞,7} 40px |- |bgcolor=#efdcc3|Dual||{7,∞,3} |- |bgcolor=#efdcc3|Coxeter group||[3,∞,7] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-7 triangular honeycomb (or 3,∞,6 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,∞,7}. It has infinitely many infinite-order triangular tiling, {3,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many infinite-order triangular tilings existing around each vertex in an order-7 apeirogonal tiling, {∞,7}, vertex figure.

{| class=wikitable

|240px
Ideal surface |}

Order-infinite-infinite triangular honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=240 !bgcolor=#efdcc3 colspan=2|Order-infinite-infinite triangular honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{3,∞,∞}
{3,(∞,∞,∞)} |- |bgcolor=#efdcc3|Coxeter diagrams||
= |- |bgcolor=#efdcc3|Cells||{3,∞} 40px |- |bgcolor=#efdcc3|Faces||{3} |- |bgcolor=#efdcc3|Edge figure||{∞} |- |bgcolor=#efdcc3|Vertex figure||{∞,∞} 40px
{(∞,∞,∞)} 40px |- |bgcolor=#efdcc3|Dual||{∞,∞,3} |- |bgcolor=#efdcc3|Coxeter group||[∞,∞,3]
[3,((∞,∞,∞))] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-infinite triangular honeycomb (or 3,∞,∞ honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,∞,∞}. It has infinitely many infinite-order triangular tiling, {3,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many infinite-order triangular tilings existing around each vertex in an infinite-order apeirogonal tiling, {∞,∞}, vertex figure.

{| class=wikitable width=480 |240px
Poincaré disk model |240px
Ideal surface |}

It has a second construction as a uniform honeycomb, Schläfli symbol {3,(∞,∞,∞)}, Coxeter diagram, = , with alternating types or colors of infinite-order triangular tiling cells. In Coxeter notation the half symmetry is [3,∞,∞,1⁺] = [3,((∞,∞,∞))].

Order-infinite-3 square honeycomb

{| class="wikitable" align="right" style="margin-left:10px" !bgcolor=#efdcc3 colspan=2|Order-infinite-3 square honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbol||{4,∞,3} |- |bgcolor=#efdcc3|Coxeter diagram|| |- |bgcolor=#efdcc3|Cells||{4,∞} 80px |- |bgcolor=#efdcc3|Faces||{4} |- |bgcolor=#efdcc3|Vertex figure||{∞,3} |- |bgcolor=#efdcc3|Dual||{3,∞,4} |- |bgcolor=#efdcc3|Coxeter group||[4,∞,3] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-3 square honeycomb (or 4,∞,3 honeycomb) a regular space-filling tessellation (or honeycomb). Each infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.

The Schläfli symbol of the order-infinite-3 square honeycomb is {4,∞,3}, with three infinite-order square tilings meeting at each edge. The vertex figure of this honeycomb is an order-3 apeirogonal tiling, {∞,3}.

{| class=wikitable |240px
Poincaré disk model |240px
Ideal surface |}

Order-infinite-3 pentagonal honeycomb

{| class="wikitable" align="right" style="margin-left:10px" !bgcolor=#efdcc3 colspan=2|Order-infinite-3 pentagonal honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbol||{5,∞,3} |- |bgcolor=#efdcc3|Coxeter diagram|| |- |bgcolor=#efdcc3|Cells||{5,∞} 80px |- |bgcolor=#efdcc3|Faces||{5} |- |bgcolor=#efdcc3|Vertex figure||{∞,3} |- |bgcolor=#efdcc3|Dual||{3,∞,5} |- |bgcolor=#efdcc3|Coxeter group||[5,∞,3] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-3 pentagonal honeycomb (or 5,∞,3 honeycomb) a regular space-filling tessellation (or honeycomb). Each infinite cell consists of an infinite-order pentagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.

The Schläfli symbol of the order-6-3 pentagonal honeycomb is {5,∞,3}, with three infinite-order pentagonal tilings meeting at each edge. The vertex figure of this honeycomb is a heptagonal tiling, {∞,3}.

{| class=wikitable |240px
Poincaré disk model |240px
Ideal surface |}

Order-infinite-3 hexagonal honeycomb

{| class="wikitable" align="right" style="margin-left:10px" !bgcolor=#efdcc3 colspan=2|Order-infinite-3 hexagonal honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbol||{6,∞,3} |- |bgcolor=#efdcc3|Coxeter diagram|| |- |bgcolor=#efdcc3|Cells||{6,∞} 80px |- |bgcolor=#efdcc3|Faces||{6} |- |bgcolor=#efdcc3|Vertex figure||{∞,3} |- |bgcolor=#efdcc3|Dual||{3,∞,6} |- |bgcolor=#efdcc3|Coxeter group||[6,∞,3] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-3 hexagonal honeycomb (or 6,∞,3 honeycomb) a regular space-filling tessellation (or honeycomb). Each infinite cell consists of an order-3 apeirogonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.

The Schläfli symbol of the order-infinite-3 hexagonal honeycomb is {6,∞,3}, with three infinite-order hexagonal tilings meeting at each edge. The vertex figure of this honeycomb is an order-3 apeirogonal tiling, {∞,3}.

{| class=wikitable |240px
Poincaré disk model |240px
Ideal surface |}

Order-infinite-3 heptagonal honeycomb

{| class="wikitable" align="right" style="margin-left:10px" !bgcolor=#efdcc3 colspan=2|Order-infinite-3 heptagonal honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbol||{7,∞,3} |- |bgcolor=#efdcc3|Coxeter diagram|| |- |bgcolor=#efdcc3|Cells||{7,∞} 80px |- |bgcolor=#efdcc3|Faces||{7} |- |bgcolor=#efdcc3|Vertex figure||{∞,3} |- |bgcolor=#efdcc3|Dual||{3,∞,7} |- |bgcolor=#efdcc3|Coxeter group||[7,∞,3] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-3 heptagonal honeycomb (or 7,∞,3 honeycomb) a regular space-filling tessellation (or honeycomb). Each infinite cell consists of an infinite-order heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.

The Schläfli symbol of the order-infinite-3 heptagonal honeycomb is {7,∞,3}, with three infinite-order heptagonal tilings meeting at each edge. The vertex figure of this honeycomb is an order-3 apeirogonal tiling, {∞,3}.

{| class=wikitable

|240px
Ideal surface |}

Order-infinite-3 apeirogonal honeycomb

{| class="wikitable" align="right" style="margin-left:10px" !bgcolor=#efdcc3 colspan=2|Order-infinite-3 apeirogonal honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbol||{∞,∞,3} |- |bgcolor=#efdcc3|Coxeter diagram|| |- |bgcolor=#efdcc3|Cells||{∞,∞} 80px |- |bgcolor=#efdcc3|Faces||Apeirogon {∞} |- |bgcolor=#efdcc3|Vertex figure||{∞,3} |- |bgcolor=#efdcc3|Dual||{3,∞,∞} |- |bgcolor=#efdcc3|Coxeter group||[∞,∞,3] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-3 apeirogonal honeycomb (or ∞,∞,3 honeycomb) a regular space-filling tessellation (or honeycomb). Each infinite cell consists of an infinite-order apeirogonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.

The Schläfli symbol of the apeirogonal tiling honeycomb is {∞,∞,3}, with three infinite-order apeirogonal tilings meeting at each edge. The vertex figure of this honeycomb is an infinite-order apeirogonal tiling, {∞,3}.

The "ideal surface" projection below is a plane-at-infinity, in the Poincaré half-space model of H3. It shows an Apollonian gasket pattern of circles inside a largest circle.

{| class=wikitable |240px
Poincaré disk model |240px
Ideal surface |}

Order-infinite-4 square honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=240 !bgcolor=#efdcc3 colspan=2|Order-infinite-4 square honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbol||{4,∞,4} |- |bgcolor=#efdcc3|Coxeter diagrams||
= |- |bgcolor=#efdcc3|Cells||{4,∞} 60px |- |bgcolor=#efdcc3|Faces||{4} |- |bgcolor=#efdcc3|Edge figure||{4} |- |bgcolor=#efdcc3|Vertex figure||{∞,4}
{∞,∞} |- |bgcolor=#efdcc3|Dual||self-dual |- |bgcolor=#efdcc3|Coxeter group||[4,∞,4] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-4 square honeycomb (or 4,∞,4 honeycomb) a regular space-filling tessellation (or honeycomb) with Schläfli symbol {4,∞,4}.

All vertices are ultra-ideal (existing beyond the ideal boundary) with four infinite-order square tilings existing around each edge and with an order-4 apeirogonal tiling vertex figure.

{| class=wikitable |240px
Poincaré disk model |240px
Ideal surface |}

It has a second construction as a uniform honeycomb, Schläfli symbol {4,∞^1,1}, Coxeter diagram, , with alternating types or colors of cells. In Coxeter notation the half symmetry is [4,∞,4,1⁺] = [4,∞^1,1].

Order-infinite-5 pentagonal honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=240 !bgcolor=#efdcc3 colspan=2|Order-infinite-5 pentagonal honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbol||{5,∞,5} |- |bgcolor=#efdcc3|Coxeter diagrams|| |- |bgcolor=#efdcc3|Cells||{5,∞} 60px |- |bgcolor=#efdcc3|Faces||{5} |- |bgcolor=#efdcc3|Edge figure||{5} |- |bgcolor=#efdcc3|Vertex figure||{∞,5} |- |bgcolor=#efdcc3|Dual||self-dual |- |bgcolor=#efdcc3|Coxeter group||[5,∞,5] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-5 pentagonal honeycomb (or 5,∞,5 honeycomb) a regular space-filling tessellation (or honeycomb) with Schläfli symbol {5,∞,5}.

All vertices are ultra-ideal (existing beyond the ideal boundary) with five infinite-order pentagonal tilings existing around each edge and with an order-5 apeirogonal tiling vertex figure.

{| class=wikitable |240px
Poincaré disk model |240px
Ideal surface |}

Order-infinite-6 hexagonal honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=280 !bgcolor=#efdcc3 colspan=2|Order-infinite-6 hexagonal honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{6,∞,6}
{6,(∞,3,∞)} |- |bgcolor=#efdcc3|Coxeter diagrams||
= |- |bgcolor=#efdcc3|Cells||{6,∞} 60px |- |bgcolor=#efdcc3|Faces||{6} |- |bgcolor=#efdcc3|Edge figure||{6} |- |bgcolor=#efdcc3|Vertex figure||{∞,6} 40px
{(5,3,5)} 40px |- |bgcolor=#efdcc3|Dual||self-dual |- |bgcolor=#efdcc3|Coxeter group||[6,∞,6]
[6,((∞,3,∞))] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-6 hexagonal honeycomb (or 6,∞,6 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {6,∞,6}. It has six infinite-order hexagonal tilings, {6,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many hexagonal tilings existing around each vertex in an order-6 apeirogonal tiling vertex figure.

{| class=wikitable |240px
Poincaré disk model |240px
Ideal surface |}

It has a second construction as a uniform honeycomb, Schläfli symbol {6,(∞,3,∞)}, Coxeter diagram, , with alternating types or colors of cells. In Coxeter notation the half symmetry is [6,∞,6,1⁺] = [6,((∞,3,∞))].

Order-infinite-7 heptagonal honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=280 !bgcolor=#efdcc3 colspan=2|Order-infinite-7 heptagonal honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{7,∞,7} |- |bgcolor=#efdcc3|Coxeter diagrams|| |- |bgcolor=#efdcc3|Cells||{7,∞} 60px |- |bgcolor=#efdcc3|Faces||{7} |- |bgcolor=#efdcc3|Edge figure||{7} |- |bgcolor=#efdcc3|Vertex figure||{∞,7} 40px |- |bgcolor=#efdcc3|Dual||self-dual |- |bgcolor=#efdcc3|Coxeter group||[7,∞,7] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-7 heptagonal honeycomb (or 7,∞,7 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {7,∞,7}. It has seven infinite-order heptagonal tilings, {7,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many heptagonal tilings existing around each vertex in an order-7 apeirogonal tiling vertex figure.

{| class=wikitable

|240px
Ideal surface |}

Order-infinite-infinite apeirogonal honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width=240 !bgcolor=#efdcc3 colspan=2|Order-infinite-infinite apeirogonal honeycomb |- |bgcolor=#efdcc3|Type||Regular honeycomb |- |bgcolor=#efdcc3|Schläfli symbols||{∞,∞,∞}
{∞,(∞,∞,∞)} |- |bgcolor=#efdcc3|Coxeter diagrams||
↔ |- |bgcolor=#efdcc3|Cells||{∞,∞} 60px |- |bgcolor=#efdcc3|Faces||{∞} |- |bgcolor=#efdcc3|Edge figure||{∞} |- |bgcolor=#efdcc3|Vertex figure||40px {∞,∞}
40px {(∞,∞,∞)} |- |bgcolor=#efdcc3|Dual||self-dual |- |bgcolor=#efdcc3|Coxeter group||[∞,∞,∞]
[∞,((∞,∞,∞))] |- |bgcolor=#efdcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-infinite-infinite apeirogonal honeycomb (or ∞,∞,∞ honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {∞,∞,∞}. It has infinitely many infinite-order apeirogonal tiling {∞,∞} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many infinite-order apeirogonal tilings existing around each vertex in an infinite-order apeirogonal tiling vertex figure.

{| class=wikitable |240px
Poincaré disk model |240px
Ideal surface |}

It has a second construction as a uniform honeycomb, Schläfli symbol {∞,(∞,∞,∞)}, Coxeter diagram, , with alternating types or colors of cells.

References

Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)

The Beauty of Geometry: Twelve Essays (1999), Dover Publications, , (Chapter 10, Regular Honeycombs in Hyperbolic Space ) Table III

Jeffrey R. Weeks The Shape of Space, 2nd EDition (Chapters 16–17: Geometries on Three-manifolds I, II)

George Maxwell, Sphere Packings and Hyperbolic Reflection Groups, JOURNAL OF ALGEBRA 79,78-97 (1982)

Hao Chen, Jean-Philippe Labbé, Lorentzian Coxeter groups and Boyd-Maxwell ball packings, (2013)

Visualizing Hyperbolic Honeycombs arXiv:1511.02851 Roice Nelson, Henry Segerman (2015)

External links

Hyperbolic Catacombs Carousel: {3,∞,3} honeycomb YouTube, Roice Nelson

John Baez, Visual insights: {7,3,3} Honeycomb (2014/08/01) {7,3,3} Honeycomb Meets Plane at Infinity (2014/08/14)

Danny Calegari, Kleinian, a tool for visualizing Kleinian groups, Geometry and the Imagination 4 March 2014.

🪦 Wikipedia History

8.5 yearsage

13editors

60edits

Archive Provenance

Created: September 28, 2017

Wikipedia title: Order-infinite-3 triangular honeycomb

Original author: Tomruen

Original author ID: 63601

Last editor: RaisedArizona

Last editor ID: 46105410

Last edit: June 9, 2026

Deleted: June 17, 2026

Verify: Verify deletion on Wikipedia →

Article size: 31.6 KB

Technical Metadata

Wikipedia page ID: 55368041

Last revision ID: 1358633070

SHA-1 hash: 07b87ac3e17ed65a623021d09dacae8632dfc8d4

Metadata captured: June 9, 2026 8:00 PM

Metadata updated: June 9, 2026 8:01 PM

📊 Wikipedia Stats

Views before deletion: 22,310

Wikipedia pages linked here: 22

Wikidata: Q48784538 (Order-infinite-3 triangular honeycomb)

All Access: 11,155 views · 106 months · September 2017 to June 2026

Desktop: 8,122 views · 106 months · September 2017 to June 2026

Mobile App: 58 views · 106 months · September 2017 to June 2026

Mobile Web: 2,975 views · 106 months · September 2017 to June 2026

View monthly pageviews (424)

June 2026 · All Access · 15 views

June 2026 · Desktop · 14 views

June 2026 · Mobile Web · 1 views

June 2026 · Mobile App · 0 views

May 2026 · All Access · 127 views

May 2026 · Desktop · 101 views

May 2026 · Mobile Web · 25 views

May 2026 · Mobile App · 1 views

April 2026 · All Access · 265 views

April 2026 · Desktop · 237 views

April 2026 · Mobile Web · 28 views

April 2026 · Mobile App · 0 views

March 2026 · All Access · 158 views

March 2026 · Desktop · 121 views

March 2026 · Mobile Web · 37 views

March 2026 · Mobile App · 0 views

February 2026 · All Access · 162 views

February 2026 · Desktop · 136 views

February 2026 · Mobile Web · 25 views

February 2026 · Mobile App · 1 views

January 2026 · All Access · 256 views

January 2026 · Desktop · 220 views

January 2026 · Mobile Web · 35 views

January 2026 · Mobile App · 1 views

December 2025 · All Access · 235 views

December 2025 · Desktop · 187 views

December 2025 · Mobile Web · 39 views

December 2025 · Mobile App · 9 views

November 2025 · All Access · 173 views

November 2025 · Desktop · 125 views

November 2025 · Mobile Web · 47 views

November 2025 · Mobile App · 1 views

October 2025 · All Access · 101 views

October 2025 · Desktop · 74 views

October 2025 · Mobile Web · 26 views

October 2025 · Mobile App · 1 views

September 2025 · All Access · 155 views

September 2025 · Desktop · 120 views

September 2025 · Mobile Web · 35 views

September 2025 · Mobile App · 0 views

August 2025 · All Access · 438 views

August 2025 · Desktop · 101 views

August 2025 · Mobile Web · 336 views

August 2025 · Mobile App · 1 views

July 2025 · All Access · 173 views

July 2025 · Desktop · 154 views

July 2025 · Mobile Web · 19 views

July 2025 · Mobile App · 0 views

June 2025 · All Access · 230 views

June 2025 · Desktop · 181 views

June 2025 · Mobile Web · 49 views

June 2025 · Mobile App · 0 views

May 2025 · All Access · 279 views

May 2025 · Desktop · 161 views

May 2025 · Mobile Web · 115 views

May 2025 · Mobile App · 3 views

April 2025 · All Access · 126 views

April 2025 · Desktop · 82 views

April 2025 · Mobile Web · 44 views

April 2025 · Mobile App · 0 views

March 2025 · All Access · 148 views

March 2025 · Desktop · 110 views

March 2025 · Mobile Web · 38 views

March 2025 · Mobile App · 0 views

February 2025 · All Access · 93 views

February 2025 · Desktop · 68 views

February 2025 · Mobile Web · 25 views

February 2025 · Mobile App · 0 views

January 2025 · All Access · 89 views

January 2025 · Desktop · 56 views

January 2025 · Mobile Web · 33 views

January 2025 · Mobile App · 0 views

December 2024 · All Access · 96 views

December 2024 · Desktop · 71 views

December 2024 · Mobile Web · 25 views

December 2024 · Mobile App · 0 views

November 2024 · All Access · 93 views

November 2024 · Desktop · 61 views

November 2024 · Mobile Web · 32 views

November 2024 · Mobile App · 0 views

October 2024 · All Access · 68 views

October 2024 · Desktop · 40 views

October 2024 · Mobile Web · 28 views

October 2024 · Mobile App · 0 views

September 2024 · All Access · 104 views

September 2024 · Desktop · 73 views

September 2024 · Mobile Web · 29 views

September 2024 · Mobile App · 2 views

August 2024 · All Access · 106 views

August 2024 · Desktop · 74 views

August 2024 · Mobile Web · 32 views

August 2024 · Mobile App · 0 views

July 2024 · All Access · 211 views

July 2024 · Desktop · 114 views

July 2024 · Mobile Web · 95 views

July 2024 · Mobile App · 2 views

June 2024 · All Access · 163 views

June 2024 · Desktop · 121 views

June 2024 · Mobile Web · 39 views

June 2024 · Mobile App · 3 views

May 2024 · All Access · 83 views

May 2024 · Desktop · 59 views

May 2024 · Mobile Web · 24 views

May 2024 · Mobile App · 0 views

April 2024 · All Access · 67 views

April 2024 · Desktop · 45 views

April 2024 · Mobile Web · 21 views

April 2024 · Mobile App · 1 views

March 2024 · All Access · 110 views

March 2024 · Desktop · 77 views

March 2024 · Mobile Web · 33 views

March 2024 · Mobile App · 0 views

February 2024 · All Access · 151 views

February 2024 · Desktop · 132 views

February 2024 · Mobile Web · 19 views

February 2024 · Mobile App · 0 views

January 2024 · All Access · 115 views

January 2024 · Desktop · 82 views

January 2024 · Mobile Web · 33 views

January 2024 · Mobile App · 0 views

December 2023 · All Access · 63 views

December 2023 · Desktop · 43 views

December 2023 · Mobile Web · 18 views

December 2023 · Mobile App · 2 views

November 2023 · All Access · 74 views

November 2023 · Desktop · 52 views

November 2023 · Mobile Web · 22 views

November 2023 · Mobile App · 0 views

October 2023 · All Access · 100 views

October 2023 · Desktop · 65 views

October 2023 · Mobile Web · 35 views

October 2023 · Mobile App · 0 views

September 2023 · All Access · 75 views

September 2023 · Desktop · 49 views

September 2023 · Mobile Web · 26 views

September 2023 · Mobile App · 0 views

August 2023 · All Access · 101 views

August 2023 · Desktop · 51 views

August 2023 · Mobile Web · 50 views

August 2023 · Mobile App · 0 views

July 2023 · All Access · 129 views

July 2023 · Desktop · 95 views

July 2023 · Mobile Web · 34 views

July 2023 · Mobile App · 0 views

June 2023 · All Access · 94 views

June 2023 · Desktop · 52 views

June 2023 · Mobile Web · 40 views

June 2023 · Mobile App · 2 views

May 2023 · All Access · 61 views

May 2023 · Desktop · 37 views

May 2023 · Mobile Web · 24 views

May 2023 · Mobile App · 0 views

April 2023 · All Access · 93 views

April 2023 · Desktop · 61 views

April 2023 · Mobile Web · 32 views

April 2023 · Mobile App · 0 views

March 2023 · All Access · 99 views

March 2023 · Desktop · 71 views

March 2023 · Mobile Web · 28 views

March 2023 · Mobile App · 0 views

February 2023 · All Access · 64 views

February 2023 · Desktop · 42 views

February 2023 · Mobile Web · 21 views

February 2023 · Mobile App · 1 views

January 2023 · All Access · 74 views

January 2023 · Desktop · 47 views

January 2023 · Mobile Web · 27 views

January 2023 · Mobile App · 0 views

December 2022 · All Access · 200 views

December 2022 · Desktop · 71 views

December 2022 · Mobile Web · 126 views

December 2022 · Mobile App · 3 views

November 2022 · All Access · 95 views

November 2022 · Desktop · 59 views

November 2022 · Mobile Web · 35 views

November 2022 · Mobile App · 1 views

October 2022 · All Access · 111 views

October 2022 · Desktop · 86 views

October 2022 · Mobile Web · 25 views

October 2022 · Mobile App · 0 views

September 2022 · All Access · 102 views

September 2022 · Desktop · 70 views

September 2022 · Mobile Web · 31 views

September 2022 · Mobile App · 1 views

August 2022 · All Access · 68 views

August 2022 · Desktop · 56 views

August 2022 · Mobile Web · 12 views

August 2022 · Mobile App · 0 views

July 2022 · All Access · 95 views

July 2022 · Desktop · 72 views

July 2022 · Mobile Web · 21 views

July 2022 · Mobile App · 2 views

June 2022 · All Access · 87 views

June 2022 · Desktop · 70 views

June 2022 · Mobile Web · 17 views

June 2022 · Mobile App · 0 views

May 2022 · All Access · 100 views

May 2022 · Desktop · 73 views

May 2022 · Mobile Web · 27 views

May 2022 · Mobile App · 0 views

April 2022 · All Access · 89 views

April 2022 · Desktop · 70 views

April 2022 · Mobile Web · 19 views

April 2022 · Mobile App · 0 views

March 2022 · All Access · 96 views

March 2022 · Desktop · 66 views

March 2022 · Mobile Web · 30 views

March 2022 · Mobile App · 0 views

February 2022 · All Access · 79 views

February 2022 · Desktop · 64 views

February 2022 · Mobile Web · 15 views

February 2022 · Mobile App · 0 views

January 2022 · All Access · 144 views

January 2022 · Desktop · 83 views

January 2022 · Mobile Web · 60 views

January 2022 · Mobile App · 1 views

December 2021 · All Access · 106 views

December 2021 · Desktop · 75 views

December 2021 · Mobile Web · 31 views

December 2021 · Mobile App · 0 views

November 2021 · All Access · 90 views

November 2021 · Desktop · 67 views

November 2021 · Mobile Web · 23 views

November 2021 · Mobile App · 0 views

October 2021 · All Access · 68 views

October 2021 · Desktop · 54 views

October 2021 · Mobile Web · 14 views

October 2021 · Mobile App · 0 views

September 2021 · All Access · 67 views

September 2021 · Desktop · 50 views

September 2021 · Mobile Web · 17 views

September 2021 · Mobile App · 0 views

August 2021 · All Access · 94 views

August 2021 · Desktop · 69 views

August 2021 · Mobile Web · 25 views

August 2021 · Mobile App · 0 views

July 2021 · All Access · 91 views

July 2021 · Desktop · 64 views

July 2021 · Mobile Web · 27 views

July 2021 · Mobile App · 0 views

June 2021 · All Access · 87 views

June 2021 · Desktop · 53 views

June 2021 · Mobile Web · 32 views

June 2021 · Mobile App · 2 views

May 2021 · All Access · 109 views

May 2021 · Desktop · 79 views

May 2021 · Mobile Web · 29 views

May 2021 · Mobile App · 1 views

April 2021 · All Access · 100 views

April 2021 · Desktop · 66 views

April 2021 · Mobile Web · 34 views

April 2021 · Mobile App · 0 views

March 2021 · All Access · 77 views

March 2021 · Desktop · 54 views

March 2021 · Mobile Web · 21 views

March 2021 · Mobile App · 2 views

February 2021 · All Access · 71 views

February 2021 · Desktop · 49 views

February 2021 · Mobile Web · 22 views

February 2021 · Mobile App · 0 views

January 2021 · All Access · 77 views

January 2021 · Desktop · 64 views

January 2021 · Mobile Web · 12 views

January 2021 · Mobile App · 1 views

December 2020 · All Access · 83 views

December 2020 · Desktop · 63 views

December 2020 · Mobile Web · 20 views

December 2020 · Mobile App · 0 views

November 2020 · All Access · 84 views

November 2020 · Desktop · 70 views

November 2020 · Mobile Web · 13 views

November 2020 · Mobile App · 1 views

October 2020 · All Access · 64 views

October 2020 · Desktop · 57 views

October 2020 · Mobile Web · 7 views

October 2020 · Mobile App · 0 views

September 2020 · All Access · 69 views

September 2020 · Desktop · 56 views

September 2020 · Mobile Web · 13 views

September 2020 · Mobile App · 0 views

August 2020 · All Access · 62 views

August 2020 · Desktop · 44 views

August 2020 · Mobile Web · 17 views

August 2020 · Mobile App · 1 views

July 2020 · All Access · 59 views

July 2020 · Desktop · 57 views

July 2020 · Mobile Web · 2 views

July 2020 · Mobile App · 0 views

June 2020 · All Access · 54 views

June 2020 · Desktop · 43 views

June 2020 · Mobile Web · 11 views

June 2020 · Mobile App · 0 views

May 2020 · All Access · 97 views

May 2020 · Desktop · 73 views

May 2020 · Mobile Web · 24 views

May 2020 · Mobile App · 0 views

April 2020 · All Access · 75 views

April 2020 · Desktop · 57 views

April 2020 · Mobile Web · 17 views

April 2020 · Mobile App · 1 views

March 2020 · All Access · 54 views

March 2020 · Desktop · 50 views

March 2020 · Mobile Web · 4 views

March 2020 · Mobile App · 0 views

February 2020 · All Access · 73 views

February 2020 · Desktop · 66 views

February 2020 · Mobile Web · 7 views

February 2020 · Mobile App · 0 views

January 2020 · All Access · 69 views

January 2020 · Desktop · 51 views

January 2020 · Mobile Web · 17 views

January 2020 · Mobile App · 1 views

December 2019 · All Access · 68 views

December 2019 · Desktop · 61 views

December 2019 · Mobile Web · 7 views

December 2019 · Mobile App · 0 views

November 2019 · All Access · 84 views

November 2019 · Desktop · 70 views

November 2019 · Mobile Web · 14 views

November 2019 · Mobile App · 0 views

October 2019 · All Access · 74 views

October 2019 · Desktop · 58 views

October 2019 · Mobile Web · 16 views

October 2019 · Mobile App · 0 views

September 2019 · All Access · 76 views

September 2019 · Desktop · 57 views

September 2019 · Mobile Web · 19 views

September 2019 · Mobile App · 0 views

August 2019 · All Access · 55 views

August 2019 · Desktop · 49 views

August 2019 · Mobile Web · 6 views

August 2019 · Mobile App · 0 views

July 2019 · All Access · 49 views

July 2019 · Desktop · 33 views

July 2019 · Mobile Web · 15 views

July 2019 · Mobile App · 1 views

June 2019 · All Access · 44 views

June 2019 · Desktop · 41 views

June 2019 · Mobile Web · 3 views

June 2019 · Mobile App · 0 views

May 2019 · All Access · 78 views

May 2019 · Desktop · 63 views

May 2019 · Mobile Web · 15 views

May 2019 · Mobile App · 0 views

April 2019 · All Access · 71 views

April 2019 · Desktop · 59 views

April 2019 · Mobile Web · 12 views

April 2019 · Mobile App · 0 views

March 2019 · All Access · 72 views

March 2019 · Desktop · 54 views

March 2019 · Mobile Web · 17 views

March 2019 · Mobile App · 1 views

February 2019 · All Access · 60 views

February 2019 · Desktop · 47 views

February 2019 · Mobile Web · 13 views

February 2019 · Mobile App · 0 views

January 2019 · All Access · 82 views

January 2019 · Desktop · 68 views

January 2019 · Mobile Web · 13 views

January 2019 · Mobile App · 1 views

December 2018 · All Access · 57 views

December 2018 · Desktop · 48 views

December 2018 · Mobile Web · 9 views

December 2018 · Mobile App · 0 views

November 2018 · All Access · 66 views

November 2018 · Desktop · 51 views

November 2018 · Mobile Web · 15 views

November 2018 · Mobile App · 0 views

October 2018 · All Access · 66 views

October 2018 · Desktop · 43 views

October 2018 · Mobile Web · 23 views

October 2018 · Mobile App · 0 views

September 2018 · All Access · 78 views

September 2018 · Desktop · 63 views

September 2018 · Mobile Web · 13 views

September 2018 · Mobile App · 2 views

August 2018 · All Access · 92 views

August 2018 · Desktop · 73 views

August 2018 · Mobile Web · 18 views

August 2018 · Mobile App · 1 views

July 2018 · All Access · 61 views

July 2018 · Desktop · 48 views

July 2018 · Mobile Web · 12 views

July 2018 · Mobile App · 1 views

June 2018 · All Access · 95 views

June 2018 · Desktop · 59 views

June 2018 · Mobile Web · 36 views

June 2018 · Mobile App · 0 views

May 2018 · All Access · 70 views

May 2018 · Desktop · 52 views

May 2018 · Mobile Web · 18 views

May 2018 · Mobile App · 0 views

April 2018 · All Access · 65 views

April 2018 · Desktop · 41 views

April 2018 · Mobile Web · 24 views

April 2018 · Mobile App · 0 views

March 2018 · All Access · 60 views

March 2018 · Desktop · 52 views

March 2018 · Mobile Web · 6 views

March 2018 · Mobile App · 2 views

February 2018 · All Access · 57 views

February 2018 · Desktop · 52 views

February 2018 · Mobile Web · 5 views

February 2018 · Mobile App · 0 views

January 2018 · All Access · 98 views

January 2018 · Desktop · 91 views

January 2018 · Mobile Web · 7 views

January 2018 · Mobile App · 0 views

December 2017 · All Access · 101 views

December 2017 · Desktop · 88 views

December 2017 · Mobile Web · 13 views

December 2017 · Mobile App · 0 views

November 2017 · All Access · 99 views

November 2017 · Desktop · 85 views

November 2017 · Mobile Web · 14 views

November 2017 · Mobile App · 0 views

October 2017 · All Access · 114 views

October 2017 · Desktop · 87 views

October 2017 · Mobile Web · 27 views

October 2017 · Mobile App · 0 views

September 2017 · All Access · 400 views

September 2017 · Desktop · 396 views

September 2017 · Mobile Web · 4 views

September 2017 · Mobile App · 0 views

Subject Tags

Regular 3-honeycombsWebarchive template wayback links

Maintenance Categories

View maintenance categories (1)

Articles for deletion

Top Contributors

View full contributor metadata (13)

Tomruen · 44 edits · user ID 63601 · first Sep 28, 2017 · last Sep 29, 2017

Mcoupal · 3 edits · user ID 8519392 · first Jan 27, 2019 · last Jan 27, 2019

InternetArchiveBot · 2 edits · user ID 27015025 · first Apr 26, 2020 · last Aug 22, 2025

LaundryPizza03 · 2 edits · user ID 32694456 · first Jul 24, 2024 · last Aug 3, 2024

BD2412 · 1 edit · user ID 196446 · first Jan 28, 2024 · last Jan 28, 2024

Beland · 1 edit · user ID 57939 · first Aug 15, 2018 · last Aug 15, 2018

Goomba1729 · 1 edit · user ID 39498513 · first Dec 1, 2021 · last Dec 1, 2021

KolbertBot · 1 edit · user ID 31691822 · first Jan 26, 2018 · last Jan 26, 2018

Myasuda · 1 edit · user ID 1187538 · first Apr 6, 2019 · last Apr 6, 2019

Parcly Taxel · 1 edit · user ID 13854216 · first Feb 21, 2020 · last Feb 21, 2020

RaisedArizona · 1 edit · user ID 46105410 · first Jun 9, 2026 · last Jun 9, 2026

Roice3 · 1 edit · user ID 1718086 · first Sep 28, 2017 · last Sep 28, 2017

Sun Creator · 1 edit · user ID 5663757 · first Dec 8, 2019 · last Dec 8, 2019

Also Known As

Order-infinite-3 apeirogonal honeycombOrder-infinite-3 heptagonal honeycombOrder-infinite-3 hexagonal honeycombOrder-infinite-3 pentagonal honeycombOrder-infinite-3 square honeycombOrder-infinite-4 square honeycombOrder-infinite-4 triangular honeycombOrder-infinite-5 pentagonal honeycombOrder-infinite-5 triangular honeycombOrder-infinite-6 hexagonal honeycombOrder-infinite-6 triangular honeycombOrder-infinite-7 heptagonal honeycombOrder-infinite-7 triangular honeycombOrder-infinite-infinite apeirogonal honeycombOrder-infinite-infinite triangular honeycombOrder-infinity-4 triangular honeycombOrder-infinity-5 triangular honeycombOrder-infinity-6 triangular honeycomb

View redirect record details

Order-infinite-3 apeirogonal honeycomb · page ID 55368624 · Article

Order-infinite-3 heptagonal honeycomb · page ID 55372455 · Article

Order-infinite-3 hexagonal honeycomb · page ID 55368617 · Article

Order-infinite-3 pentagonal honeycomb · page ID 55368611 · Article

Order-infinite-3 square honeycomb · page ID 55368604 · Article

Order-infinite-4 square honeycomb · page ID 55368633 · Article

Order-infinite-4 triangular honeycomb · page ID 55368813 · Article

Order-infinite-5 pentagonal honeycomb · page ID 55368639 · Article

Order-infinite-5 triangular honeycomb · page ID 55368826 · Article

Order-infinite-6 hexagonal honeycomb · page ID 55368644 · Article

Order-infinite-6 triangular honeycomb · page ID 55368849 · Article

Order-infinite-7 heptagonal honeycomb · page ID 55371827 · Article

Order-infinite-7 triangular honeycomb · page ID 55372451 · Article

Order-infinite-infinite apeirogonal honeycomb · page ID 55345015 · Article

Order-infinite-infinite triangular honeycomb · page ID 55368596 · Article

Order-infinity-4 triangular honeycomb · page ID 55368574 · Article

Order-infinity-5 triangular honeycomb · page ID 55368579 · Article

Order-infinity-6 triangular honeycomb · page ID 55368587 · Article

Why Deleted

AfD

"'''Delete''', this is a major WP:CALC situation. Showing up in tables is not indicative of notability, and assembling several distinct polytopes into one article as "related" doesn't change that. All relevant data already contained at List of regular polytopes#4 apeirotopes (look for the correspo..." Read more

Nominated by RaisedArizona

by Sandstein

Articles for deletion/Order-infinite-3 triangular honeycomb (XFDcloser)

View AfD discussion ↗

Wikipedia Assessment

Science (Unknown)

View all assessment records (1)

Science · importance Unknown

Sources

blogs.ams.org/...

lamington.wordpress.com/...

Additional preserved links are available in the archive details below.

Archive Inventory

View stored source record counts

Revision rows stored: 60

Outgoing links stored: 57

External links stored: 17

Templates stored: 34

Talk exports stored: 1

AfD exports stored: 1

Raw API payloads stored: 14

Image records stored: 10

View full source metadata

Outgoing Wikipedia links (57)

ApeirogonApeirogonal tilingApollonian gasketCell (geometry)Convex uniform honeycombs in hyperbolic spaceCoxeter diagramCoxeter notationCoxeter-Dynkin diagramCoxeter–Dynkin diagramDanny CalegariGeometryH. S. M. CoxeterHeptagonHeptagonal tilingHexagonHoneycomb (geometry)Hyperbolic spaceHypercycle (geometry)Infinite-order apeirogonal tilingInfinite-order heptagonal tilingInfinite-order hexagonal tilingInfinite-order pentagonal tilingInfinite-order square tilingInfinite-order triangular tilingISBN (identifier)Jeffrey Weeks (mathematician)John BaezLCCN (identifier)List of regular polytopesOrder-3 apeirogonal tilingOrder-4 apeirogonal tilingOrder-5 apeirogonal tilingOrder-5 heptagonal tilingOrder-6 apeirogonal tilingOrder-6 hexagonal tilingOrder-7 apeirogonal tilingOrder-infinite-3 apeirogonal honeycombOrder-infinite-3 heptagonal honeycombOrder-infinite-3 hexagonal honeycombOrder-infinite-3 pentagonal honeycombOrder-infinite-3 square honeycombOrder-infinite-4 triangular honeycombOrder-infinite-5 triangular honeycombOrder-infinite-6 triangular honeycombOrder-infinite-7 triangular honeycombOrder-infinite-infinite triangular honeycombPentagonPoincaré disk modelRegular Polytopes (book)Schläfli symbolSquareTessellationTriangleVertex figureVertex figuresWayback MachineYouTube

Backlinks (22)

5-cellIcosahedral honeycombList of regular polytopesOrder-infinite-3 apeirogonal honeycombOrder-infinite-3 heptagonal honeycombOrder-infinite-3 hexagonal honeycombOrder-infinite-3 pentagonal honeycombOrder-infinite-3 square honeycombOrder-infinite-4 square honeycombOrder-infinite-4 triangular honeycombOrder-infinite-5 pentagonal honeycombOrder-infinite-5 triangular honeycombOrder-infinite-6 hexagonal honeycombOrder-infinite-6 triangular honeycombOrder-infinite-7 heptagonal honeycombOrder-infinite-7 triangular honeycombOrder-infinite-infinite apeirogonal honeycombOrder-infinite-infinite triangular honeycombOrder-infinity-4 triangular honeycombOrder-infinity-5 triangular honeycombOrder-infinity-6 triangular honeycombTriangular tiling honeycomb

External links (17)

blogs.ams.org/...

lamington.wordpress.com/...

www.mathunion.org/...

www.sciencedirect.com/...

https://arxiv.org/abs/1310.8608

https://arxiv.org/abs/1511.02851

scholar.google.com/...

web.archive.org/...

www.google.com/...

www.jstor.org/...

https://www.loc.gov/item/99035678

https://www.youtube.com/watch?v=GRo_FQm2KRc

Templates (34)

AmboxArticle for deletion/datedArticle for deletion/switchCDDClearCoxeter–Dynkin diagramFind sources mainspaceISBNLCCNLibrary of Congress Control NumberMain otherModule:ArgumentsModule:Check for unknown parametersModule:Citation/CS1/ConfigurationModule:Citation/CS1/IdentifiersModule:Citation/CS1/styles.cssModule:Citation/CS1/UtilitiesModule:Coxeter–Dynkin diagramModule:CS1 identifiersModule:Find sourcesModule:Find sources/configModule:Find sources/linksModule:Find sources/templates/Find sources mainspaceModule:LCCNModule:Message boxModule:Message box/ambox.cssModule:Message box/configurationModule:WebarchiveModule:Webarchive/dataModule:YesnoNOINDEXReflistReflist/styles.cssWebarchive

📊 Wikidata

Subject Facts

QID: Q48784538

Label: Order-infinite-3 triangular honeycomb

Wikidata Archive Data

Captured: June 9, 2026 8:01 PM

View raw claims JSON

Stored properties: 1

P2671

{
    "P2671": [
        {
            "id": "Q48784538$77D34D29-1CAD-406D-A6A1-96576A0B536A",
            "rank": "normal",
            "type": "statement",
            "mainsnak": {
                "hash": "d4c0a605b81a02b639d0ac696f29255c8b05af93",
                "datatype": "external-id",
                "property": "P2671",
                "snaktype": "value",
                "datavalue": {
                    "type": "string",
                    "value": "/g/11fz9d3h_l"
                }
            }
        }
    ]
}

Main Menu

Order-infinite-3 triangular honeycomb

Geometry

Related polytopes and honeycombs

Order-infinite-4 triangular honeycomb

Order-infinite-5 triangular honeycomb

Order-infinite-6 triangular honeycomb

Order-infinite-7 triangular honeycomb

Order-infinite-infinite triangular honeycomb

Order-infinite-3 square honeycomb

Order-infinite-3 pentagonal honeycomb

Order-infinite-3 hexagonal honeycomb

Order-infinite-3 heptagonal honeycomb

Order-infinite-3 apeirogonal honeycomb

Order-infinite-4 square honeycomb

Order-infinite-5 pentagonal honeycomb

Order-infinite-6 hexagonal honeycomb

Order-infinite-7 heptagonal honeycomb

Order-infinite-infinite apeirogonal honeycomb

See also

References

External links