In geometry, there are a sequence of regular polytopes and honeycombs, {4,3,p}, with cubic cells. The first is the finite tesseract in 4-dimensional space. The second is the cubic honeycomb that tessellates Euclidean 3-space. The next two tessellate hyperbolic 3-space.
{4,3,p} regular honeycombs | |||||||||||
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Space | S3 | E3 | H3 | ||||||||
Form | Finite | Affine | Compact | Paracompact | Noncompact | ||||||
Name![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{4,3,3}![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{4,3,4}![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{4,3,5}![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{4,3,6}![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{4,3,7}![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{4,3,8}![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
...
{4,3,∞}![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ||||
Image |
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Vertex figure ![]() ![]() ![]() ![]() ![]() |
![]() {3,3} ![]() ![]() ![]() ![]() ![]() |
![]() {3,4} ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() {3,5} ![]() ![]() ![]() ![]() ![]() |
![]() {3,6} ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() {3,7} ![]() ![]() ![]() ![]() ![]() |
![]() {3,8} ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() {3,∞} ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |