Cyclotruncated 7-simplex honeycomb | |
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(No image) | |
Type | Uniform honeycomb |
Family | Cyclotruncated simplectic honeycomb |
Schläfli symbol | t0,1{3[8]} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-face types |
{36}
![]() t0,1{36} ![]() t1,2{36} ![]() t2,3{36} ![]() |
Vertex figure | Elongated 6-simplex antiprism |
Symmetry | ×22, [[3[8]]] |
Properties | vertex-transitive |
In seven-dimensional Euclidean geometry, the cyclotruncated 7-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 7-simplex, truncated 7-simplex, bitruncated 7-simplex, and tritruncated 7-simplex facets. These facet types occur in proportions of 1:1:1:1 respectively in the whole honeycomb.
It can be constructed by eight sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 6-simplex honeycomb divisions on each hyperplane.
This honeycomb is one of 29 unique uniform honeycombs [1] constructed by the Coxeter group, grouped by their extended symmetry of rings within the regular octagon diagram:
A7 honeycombs | ||||
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Octagon symmetry |
Extended symmetry |
Extended diagram |
Extended group |
Honeycombs |
a1
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[3[8]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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d2
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<[3[8]]> | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
×21 |
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p2
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[[3[8]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
×22 | |
d4
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<2[3[8]]> | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
×41 |
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p4
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[2[3[8]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
×42 |
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d8
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[4[3[8]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
×8 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
r16
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[8[3[8]]] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
×16 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Regular and uniform honeycombs in 7-space:
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 |