Category:Regular tessellations

See also Honeycomb (geometry), Regular honeycomb, Regular tiling, Tessellation, https://en.wikipedia.org/wiki/Category:Regular_tilings .

In two-dimensions, honeycombs are called tilings or tessellations.

By dimensions 2 thru 8, the only regular honeycombs are:

2-D:

• Triangular tiling (dual to Hexagonal tiling)
• Square tiling (self-dual)
• Hexagonal tiling (dual to Triangular tiling)

3-D:

• Cubic honeycomb (self-dual)

4-D:

• 4-cubic honeycomb (Tesseractic honeycomb) (self-dual)
• 16-cell honeycomb (dual to 24-cell honeycomb)
• 24-cell honeycomb (dual to 16-cell honeycomb)

5-D:

• 5-cubic honeycomb (self-dual)

6-D:

• 6-cubic honeycomb (self-dual)

7-D:

• 7-cubic honeycomb (self-dual)

8-D:

• 8-cubic honeycomb (self-dual)

(see also https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds#Euclidean_tilings , https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds#Three_dimensions_(4-apeirotopes) , https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds#Tessellations_of_Euclidean_4-space , https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds#Tessellations_of_Euclidean_5-space , https://en.wikipedia.org/wiki/Euclidean_tilings_by_convex_regular_polygons )