Bitruncated 16-cell honeycomb

In four-dimensional Euclidean geometry, the bitruncated 16-cell honeycomb (or runcicantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.

Bitruncated 16-cell honeycomb
(No image)
Type	Uniform honeycomb
Schläfli symbol	t1,2{3,3,4,3} h2,3{4,3,3,4} 2t{3,31,1,1}
Coxeter-Dynkin diagram	= =
4-face type	Truncated 24-cell Bitruncated tesseract
Cell type	Cube Truncated octahedron Truncated tetrahedron
Face type	{3}, {4}, {6}
Vertex figure
Coxeter group	${\displaystyle {\tilde {F}}_{4}}$ = [3,3,4,3] ${\displaystyle {\tilde {B}}_{4}}$ = [4,3,31,1] ${\displaystyle {\tilde {D}}_{4}}$ = [31,1,1,1]
Dual	?
Properties	vertex-transitive

Symmetry constructions

There are 3 different symmetry constructions, all with 3-3 duopyramid vertex figures. The ${\displaystyle {\tilde {B}}_{4}}$ symmetry doubles on ${\displaystyle {\tilde {D}}_{4}}$ in three possible ways, while ${\displaystyle {\tilde {F}}_{4}}$ contains the highest symmetry.

Affine Coxeter group	${\displaystyle {\tilde {F}}_{4}}$ [3,3,4,3]	${\displaystyle {\tilde {B}}_{4}}$ [4,3,31,1]	${\displaystyle {\tilde {D}}_{4}}$ [31,1,1,1]
Coxeter diagram
4-faces

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