Order-5 tesseractic honeycomb | |
---|---|
(No image) | |
Type | Hyperbolic regular honeycomb |
Schläfli symbol | {4,3,3,5} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4-faces |
![]() |
Cells |
![]() |
Faces |
![]() |
Face figure |
![]() |
Edge figure |
![]() |
Vertex figure |
![]() |
Dual | Order-4 120-cell honeycomb |
Coxeter group | BH4, [5,3,3,4] |
Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 tesseractic honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {4,3,3,5}, it has five 8-cells (also known as tesseracts) around each face. Its dual is the order-4 120-cell honeycomb, {5,3,3,4}.
It is related to the Euclidean 4-space (order-4) tesseractic honeycomb, {4,3,3,4}, and the 5-cube, {4,3,3,3} in Euclidean 5-space. The 5-cube can also be seen as an order-3 tesseractic honeycomb on the surface of a 4-sphere.
Order-5 tesseractic honeycomb | |
---|---|
(No image) | |
Type | Hyperbolic regular honeycomb |
Schläfli symbol | {4,3,3,5} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4-faces |
![]() |
Cells |
![]() |
Faces |
![]() |
Face figure |
![]() |
Edge figure |
![]() |
Vertex figure |
![]() |
Dual | Order-4 120-cell honeycomb |
Coxeter group | BH4, [5,3,3,4] |
Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 tesseractic honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {4,3,3,5}, it has five 8-cells (also known as tesseracts) around each face. Its dual is the order-4 120-cell honeycomb, {5,3,3,4}.
It is related to the Euclidean 4-space (order-4) tesseractic honeycomb, {4,3,3,4}, and the 5-cube, {4,3,3,3} in Euclidean 5-space. The 5-cube can also be seen as an order-3 tesseractic honeycomb on the surface of a 4-sphere.