Truncated tesseractic honeycomb | |
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(No image) | |
Type | Uniform 4-honeycomb |
Schläfli symbol | t{4,3,3,4} t{4,3,31,1} |
Coxeter-Dynkin diagram | |
4-face type | truncated tesseract 16-cell |
Cell type | Truncated cube Tetrahedron |
Face type | {3}, {8} |
Vertex figure | octahedral pyramid |
Coxeter group | = [4,3,3,4] = [4,3,31,1] |
Dual | |
Properties | vertex-transitive |
In four-dimensional Euclidean geometry, the truncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a truncation of a tesseractic honeycomb creating truncated tesseracts, and adding new 16-cell facets at the original vertices.
The [4,3,3,4], , Coxeter group generates 31 permutations of uniform tessellations, 21 with distinct symmetry and 20 with distinct geometry. The expanded tesseractic honeycomb (also known as the stericated tesseractic honeycomb) is geometrically identical to the tesseractic honeycomb. Three of the symmetric honeycombs are shared in the [3,4,3,3] family. Two alternations (13) and (17), and the quarter tesseractic (2) are repeated in other families.
C4 honeycombs | |||
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Extended symmetry | Extended diagram | Order | Honeycombs |
[4,3,3,4]: | ×1 | ||
[[4,3,3,4]] | ×2 | (1) , (2) , (13) , 18 (6) , 19 , 20 | |
[(3,3)[1+,4,3,3,4,1+]] ↔ [(3,3)[31,1,1,1]] ↔ [3,4,3,3] | ↔ ↔ | ×6 |
Regular and uniform honeycombs in 4-space:
In four-dimensional Euclidean geometry, the truncated 16-cell honeycomb is a uniform space-filling tessellation in Euclidean 4-space. It is constructed by 24-cell and truncated 16-cell facets.
In four-dimensional Euclidean geometry, the rectified tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space. It is constructed by a rectification of a tesseractic honeycomb which creates new vertices on the middle of all the original edges, rectifying the cells into rectified tesseracts, and adding new 16-cell facets at the original vertices. Its vertex figure is an octahedral prism, {3,4}×{}.
In four-dimensional Euclidean geometry, the bitruncated tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space. It is constructed by a bitruncation of a tesseractic honeycomb. It is also called a cantic quarter tesseractic honeycomb from its q2{4,3,3,4} construction.
In four-dimensional Euclidean geometry, the birectified 16-cell honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the steriruncitruncated tesseractic honeycomb is a uniform space-filling honeycomb.
In four-dimensional Euclidean geometry, the stericantellated tesseractic honeycomb is a uniform space-filling honeycomb.
In four-dimensional Euclidean geometry, the omnitruncated tesseractic honeycomb is a uniform space-filling honeycomb. It has omnitruncated tesseract, truncated cuboctahedral prism, and 8-8 duoprism facets in an irregular 5-cell vertex figure.
In four-dimensional Euclidean geometry, the cantellated tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space. It is constructed by a cantellation of a tesseractic honeycomb creating cantellated tesseracts, and new 24-cell and octahedral prism facets at the original vertices.
In four-dimensional Euclidean geometry, the runcinated tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space. It is constructed by a runcination of a tesseractic honeycomb creating runcinated tesseracts, and new tesseract, rectified tesseract and cuboctahedral prism facets.
In four-dimensional Euclidean geometry, the cantitruncated tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the runcitruncated tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the steritruncated tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the runcicantitruncated tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the runcicantellated tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the stericantitruncated tesseractic honeycomb is a uniform space-filling honeycomb. It is composed of runcitruncated 16-cell, cantitruncated tesseract, rhombicuboctahedral prism, truncated cuboctahedral prism, and 4-8 duoprism facets, arranged around an irregular 5-cell vertex figure.
In four-dimensional Euclidean geometry, the steric tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the steriruncic tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the stericantic tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the steriruncicantic tesseractic honeycomb is a uniform space-filling tessellation in Euclidean 4-space.
In four-dimensional Euclidean geometry, the cantitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantitruncation of the regular 24-cell honeycomb, containing truncated tesseract, cantitruncated 24-cell, and tetrahedral prism cells.
Space | Family | / / | ||||
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E2 | Uniform tiling | {3[3]} | δ3 | hδ3 | qδ3 | Hexagonal |
E3 | Uniform convex honeycomb | {3[4]} | δ4 | hδ4 | qδ4 | |
E4 | Uniform 4-honeycomb | {3[5]} | δ5 | hδ5 | qδ5 | 24-cell honeycomb |
E5 | Uniform 5-honeycomb | {3[6]} | δ6 | hδ6 | qδ6 | |
E6 | Uniform 6-honeycomb | {3[7]} | δ7 | hδ7 | qδ7 | 222 |
E7 | Uniform 7-honeycomb | {3[8]} | δ8 | hδ8 | qδ8 | 133 • 331 |
E8 | Uniform 8-honeycomb | {3[9]} | δ9 | hδ9 | qδ9 | 152 • 251 • 521 |
E9 | Uniform 9-honeycomb | {3[10]} | δ10 | hδ10 | qδ10 | |
E10 | Uniform 10-honeycomb | {3[11]} | δ11 | hδ11 | qδ11 | |
En-1 | Uniform (n-1)-honeycomb | {3[n]} | δn | hδn | qδn | 1k2 • 2k1 • k21 |