Steric tesseractic honeycomb

In four-dimensional Euclidean geometry, the steric tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.

Steric tesseractic honeycomb
(No image)
Type	Uniform honeycomb
Schläfli symbol	h4{4,3,3,4}
Coxeter-Dynkin diagram	=
4-face type	{4,3,3} t0,3{4,3,3} {3,3,4} {3,3}×{}
Cell type	{4,3} {3,3} {3}×{}
Face type	{4} {3}
Vertex figure
Coxeter group	${\displaystyle {\tilde {B}}_{4}}$ = [4,3,31,1]
Dual	?
Properties	vertex-transitive

Alternate names

• Small diprismatodemitesseractic tetracomb (siphatit)

Related honeycombs

The [4,3,3^1,1], , Coxeter group generates 31 permutations of uniform tessellations, 23 with distinct symmetry and 4 with distinct geometry. There are two alternated forms: the alternations (19) and (24) have the same geometry as the 16-cell honeycomb and snub 24-cell honeycomb respectively.

B4 honeycombs
Extended symmetry	Extended diagram	Order	Honeycombs
[4,3,31,1]:		×1	5, 6, 7, 8
<[4,3,31,1]>: ↔[4,3,3,4]	↔	×2	9, 10, 11, 12, 13, 14, (10), 15, 16, (13), 17, 18, 19
[3[1+,4,3,31,1]] ↔ [3[3,31,1,1]] ↔ [3,3,4,3]	↔ ↔	×3	1, 2, 3, 4
[(3,3)[1+,4,3,31,1]] ↔ [(3,3)[31,1,1,1]] ↔ [3,4,3,3]	↔ ↔	×12	20, 21, 22, 23

See also

Regular and uniform honeycombs in 4-space:

• Tesseractic honeycomb
• 16-cell honeycomb
• 24-cell honeycomb
• Rectified 24-cell honeycomb
• Truncated 24-cell honeycomb
• Snub 24-cell honeycomb
• 5-cell honeycomb
• Truncated 5-cell honeycomb
• Omnitruncated 5-cell honeycomb