| Stericantitruncated 16-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform 4-honeycomb |
| Schläfli symbol | t0,1,2,4{3,3,4,3} s2,3,4{3,4,3,3} |
| Coxeter-Dynkin diagrams |      |
| 4-face type | t0,1,2{3,3,4} Contents |
| Cell type | |
| Face type | |
| Vertex figure | |
| Coxeter groups | , [3,4,3,3] |
| Properties | Vertex transitive |
In four-dimensional Euclidean geometry, the stericantitruncated 16-cell honeycomb is a uniform space-filling honeycomb.
The [3,4,3,3], , Coxeter group generates 31 permutations of uniform tessellations, 28 are unique in this family and ten are shared in the [4,3,3,4] and [4,3,31,1] families. The alternation (13) is also repeated in other families.
| F4 honeycombs | |||
|---|---|---|---|
| Extended symmetry | Extended diagram | Order | Honeycombs |
| [3,3,4,3] | | ×1 | |
| [3,4,3,3] | | ×1 |
|
| [(3,3)[3,3,4,3*]] =[(3,3)[31,1,1,1]] =[3,4,3,3] |       =  =  | ×4 | |
Regular and uniform honeycombs in 4-space:
In four-dimensional Euclidean geometry, the truncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a truncation of the regular 24-cell honeycomb, containing tesseract and truncated 24-cell cells.
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 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 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 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.
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 runcinated 16-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a runcination of the regular 16-cell honeycomb, containing Rectified 24-cell, runcinated tesseract, cuboctahedral 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 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.
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.
In four-dimensional Euclidean geometry, the runcicantellated 24-cell honeycomb is a uniform space-filling honeycomb.
| 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]} | 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 |
