Truncated tesseractic honeycomb | |
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(No image) | |
Type | Uniform 4-honeycomb |
Schläfli symbol | t{4,3,3,4} t{4,3,3^{1,1}} |
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] = [4,3,3^{1,1}] |
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],
C4 honeycombs | |||
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Extended symmetry | Extended diagram | Order | Honeycombs |
[4,3,3,4]: | ×1 | ||
[[4,3,3,4]] | ×2 | ||
[(3,3)[1^{+},4,3,3,4,1^{+}]] ↔ [(3,3)[3^{1,1,1,1}]] ↔ [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 q_{2}{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 bitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a bitruncation of the regular 24-cell honeycomb, constructed by truncated tesseract and bitruncated 24-cell cells.
Fundamental convex regular and uniform honeycombs in dimensions 2-9 | ||||||
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Space | Family | / / | ||||
E^{2} | Uniform tiling | {3^{[3]}} | δ_{3} | hδ_{3} | qδ_{3} | Hexagonal |
E^{3} | Uniform convex honeycomb | {3^{[4]}} | δ_{4} | hδ_{4} | qδ_{4} | |
E^{4} | Uniform 4-honeycomb | {3^{[5]}} | δ_{5} | hδ_{5} | qδ_{5} | 24-cell honeycomb |
E^{5} | Uniform 5-honeycomb | {3^{[6]}} | δ_{6} | hδ_{6} | qδ_{6} | |
E^{6} | Uniform 6-honeycomb | {3^{[7]}} | δ_{7} | hδ_{7} | qδ_{7} | 2_{22} |
E^{7} | Uniform 7-honeycomb | {3^{[8]}} | δ_{8} | hδ_{8} | qδ_{8} | 1_{33} • 3_{31} |
E^{8} | Uniform 8-honeycomb | {3^{[9]}} | δ_{9} | hδ_{9} | qδ_{9} | 1_{52} • 2_{51} • 5_{21} |
E^{9} | Uniform 9-honeycomb | {3^{[10]}} | δ_{10} | hδ_{10} | qδ_{10} | |
E^{n-1} | Uniform (n-1)-honeycomb | {3^{[n]}} | δ_{n} | hδ_{n} | qδ_{n} | 1_{k2} • 2_{k1} • k_{21} |