Stericantitruncated tesseractic honeycomb

Last updated
Stericantitruncated tesseractic honeycomb
(No image)
TypeUniform honeycomb
Schläfli symbol t0,1,2,4{4,3,3,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png
4-face type

runcitruncated 16-cell Schlegel half-solid runcitruncated 16-cell.png
cantitruncated tesseract Cantitruncated tesseract stella4d.png
rhombicuboctahedral prism Rhombicuboctahedral prism.png
truncated cuboctahedral prism Truncated cuboctahedral prism.png
4-8 duoprism 4-8 duoprism.png

Contents

Cell type Truncated cuboctahedron Great rhombicuboctahedron.png
Rhombicuboctahedron Small rhombicuboctahedron.png
Truncated tetrahedron Truncated tetrahedron.png
Octagonal prism Octagonal prism.png
Hexagonal prism Hexagonal prism.png
Cube Hexahedron.png
Triangular prism Triangular prism.png
Face type{3}, {4}, {6}, {8}
Vertex figure irr. square pyramid pyramid
Coxeter groups , [4,3,3,4]
Properties Vertex transitive

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.

The [4,3,3,4], CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png, 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.

See also

Regular and uniform honeycombs in 4-space:

Related Research Articles

In four-dimensional Euclidean geometry, the rectified 24-cell honeycomb is a uniform space-filling honeycomb. It is constructed by a rectification of the regular 24-cell honeycomb, containing tesseract and rectified 24-cell cells.

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 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 truncated tesseractic honeycomb is a uniform space-filling tessellation 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.

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 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 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 cantellated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantellation of the regular 24-cell honeycomb, containing rectified tesseract, cantellated 24-cell, and tetrahedral prism cells.

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.

In four-dimensional Euclidean geometry, the runcinated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a runcination of the regular 24-cell honeycomb, containing runcinated 24-cell, 24-cell, octahedral prism, and 3-3 duoprism cells.

In four-dimensional Euclidean geometry, the stericated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a sterication of the regular 24-cell honeycomb, containing 24-cell, 16-cell, octahedral prism, tetrahedral prism, and 3-3 duoprism cells.

In four-dimensional Euclidean geometry, the steritruncated 16-cell honeycomb is a uniform space-filling honeycomb, with runcinated 24-cell, truncated 16-cell, octahedral prism, 3-6 duoprism, and truncated tetrahedral prism cells.

References

Fundamental convex regular and uniform honeycombs in dimensions 2-9
Space Family / /
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]}δ10hδ10qδ10
En-1Uniform (n-1)-honeycomb {3[n]} δn hδn qδn 1k2 • 2k1 • k21
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.