Runcinated 24-cell honeycomb | |
---|---|
(No image) | |
Type | Uniform 4-honeycomb |
Schläfli symbol | t0,3{3,4,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4-face type |
t0,3{3,4,3}
![]() {3,4,3} ![]() {3,4}x{} ![]() {3}x{3} ![]() |
Cell type |
{3,4} {3}x{} |
Face type | {3}, {4} |
Vertex figure | |
Coxeter groups | , [3,4,3,3] |
Properties | Vertex transitive |
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.
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:
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 |
Runcinated 24-cell honeycomb | |
---|---|
(No image) | |
Type | Uniform 4-honeycomb |
Schläfli symbol | t0,3{3,4,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4-face type |
t0,3{3,4,3}
![]() {3,4,3} ![]() {3,4}x{} ![]() {3}x{3} ![]() |
Cell type |
{3,4} {3}x{} |
Face type | {3}, {4} |
Vertex figure | |
Coxeter groups | , [3,4,3,3] |
Properties | Vertex transitive |
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.
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:
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 |