Petrial tesseract

Petrial tesseract
Rank	4
Type	Regular
Space	Spherical
Notation
Schläfli symbol	$\{4,3,3\}^\pi$ $\{\{4,4\mid 4\},\{4,3\}_3\}$
Elements
Cells	3 square duocombs
Faces	24 squares
Edges	32
Vertices	16
Vertex figure	Petrial tetrahedron, edge length √2
Measures (edge length 1)
Circumradius	1
Related polytopes
Army	Tes
Regiment	Tes
Petrie dual	Tesseract
Abstract & topological properties
Flag count	384
Euler characteristic	5
Schläfli type	{4,4,3}
Orientable	No
Properties
Symmetry	B4, order 384
Convex	No
Net count	1

The petrial tesseract is a regular skew polychoron consisting of 3 square duocombs. It shares its faces, edges, and vertices with the tesseract, and it has a petrial tetrahedron vertex figure. It is the Petrie dual of the tesseract.

The petrial tesseract is also the only known (concrete) regular polychoron that has duocombs as cells. It is also a quotient of the square tiling honeycomb.

Vertex coordinates

The vertex coordinates of the petrial tesseract are the same as that of its regiment colonel, the tesseract.

External links

• Hartley, Michael. "{4,4,3}*384a".