Triangular tiling honeycomb: Difference between revisions

Revision as of 03:59, 24 July 2024

Latest revision as of 12:02, 10 August 2025

(11 intermediate revisions by 4 users not shown)

Line 10:

|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||{{CDD|node_1|3|node|6|node|3|node}}<BR>{{CDD|node_h1|6|node|3|node|6|node}} ↔ {{CDD|branch_10ru|split2|node|6|node}}<BR>{{CDD|node_h1|6|node|split1|branch}} ↔ {{CDD|node_1|splitsplit1|branch4|splitsplit2|node}} ↔ {{CDD|branch_10ru|split2|node|6|node_h0}}

|-

|bgcolor=#e7dcc3|Cells||[[Triangular tiling|{3,6}]] [[File:Uniform tiling 63-t2.pngsvg|40px]] [[File:Uniform tiling 333-t1.pngsvg|40px]]

|-

|bgcolor=#e7dcc3|Faces||[[triangle]] {3}

Line 16:

|bgcolor=#e7dcc3|[[Edge figure]]||[[triangle]] {3}

|-

|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Uniform tiling 63-t0.pngsvg|40px]] [[File:Uniform tiling 63-t12.pngsvg|40px]] [[File:Uniform tiling 333-t012.pngsvg|40px]]<BR>[[hexagonal tiling]]

|-

|bgcolor=#e7dcc3|[[Dual polytope|Dual]]||[[Self-dual polytope|Self-dual]]

Line 62:

|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node|3|node_1|6|node|3|node}}<BR>{{CDD|node_h1|6|node|3|node_1|6|node}} ↔ {{CDD|branch_10ru|split2|node_1|6|node}}<BR>{{CDD|node|splitsplit1|branch4_11|splitsplit2|node_1}} ↔ {{CDD|branch_10ru|split2|node_1|6|node_h0}} ↔ {{CDD|node|3|node_1|6|node_g|3sg|node_g}}

|-

|bgcolor=#e7dcc3|Cells||[[trihexagonal tiling|r{3,6}]] [[File:Uniform polyhedron-63-t1.pngsvg|40px]]<BR>[[hexagonal tiling|{6,3}]] [[File:Uniform polyhedron-63-t0.png|40px]]

|-

|bgcolor=#e7dcc3|Faces||[[triangle]] {3}<BR>[[hexagon]] {6}

Line 147:

|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_1|3|node|6|node_1|3|node}}<BR>{{CDD|node_h|3|node_h|6|node_1|3|node}}

|-

|bgcolor=#e7dcc3|Cells||[[rhombitrihexagonal tiling|rr{6,3}]] [[File:Uniform polyhedron-63-t02.png|40px]]<BR>[[trihexagonal tiling|r{6,3}]] [[File:Uniform polyhedron-63-t1.pngsvg|40px]]<BR>[[Triangular prism|{}×{3}]] [[File:Triangular prism.png|40px]]

|-

|bgcolor=#e7dcc3|Faces||[[triangle]] {3}<BR>[[square]] {4}<BR>[[hexagon]] {6}

Line 204:

|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_1|3|node|6|node|3|node_1}}

|-

|bgcolor=#e7dcc3|Cells||[[triangular tiling|{3,6}]] [[File:Uniform polyhedron-63-t2.pngsvg|40px]]<BR>[[Triangular prism|{}×{3}]] [[File:Triangular prism.png|40px]]

|-

|bgcolor=#e7dcc3|Faces||[[triangle]] {3}<BR>[[square]] {4}

Line 288:

|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_h|3|node_h|6|node|3|node_1}}

|-

|bgcolor=#e7dcc3|Cells|||[[Trihexagonal tiling|r{6,3}]] [[File:Uniform tiling 333-t02.pngsvg|40px]]<BR>[[Triangular prism|{}x{3}]] [[File:triangular prism.png|40px]]<BR>[[triangular tiling|{3,6}]] [[File:Uniform tiling 333-t1.pngsvg|40px]]<BR>[[triangular cupola|tricup]] [[File:Triangular cupola.png|40px]]

|-

|bgcolor=#e7dcc3|Faces||[[triangle]] {3}<BR>[[square]] {4}<BR>[[hexagon]] {6}

Line 315:

** N.W. Johnson: ''Geometries and Transformations'', (2018) Chapter 13: Hyperbolic Coxeter groups

[[Category:Regular 3-honeycombs]]

[[Category:Self-dual tilings]]

[[Category:Triangular tilings]]