Rank4
TypeCRF
Notation
Bowers style acronymCytau tes
Coxeter diagramox4qo ox4oo&#zx
Elements
Cells16 square pyramids, 4 octahedra, 4 cubes
Faces16+32 triangles, 4+16 squares
Edges32+16+16
Vertices4+16
Vertex figures4 cubes, edge length 1
16 halves of octahedra bisected along the square pseudo-face, edge length 1 (revealed pseudoface and bisected edges) and 2 (original edges)
Measures (edge length 1)
Hypervolume${\displaystyle {\frac {3}{2}}=1.5}$
Dichoral anglesCube–4–squippy: 135°
Oct-3-squippy: 120°
Squippy–3-squippy: 120°
Cube–4–cube: 90°
Central density1
Related polytopes
ArmyCytau tes
RegimentCytau tes
ConjugateNone
Abstract & topological properties
Flag count896
Euler characteristic0
OrientableYes
Properties
Symmetryorder 64
ConvexYes
NatureTame

The cyclotetradiminished icositetrachoron, also called the cyclotetraaugmented tesseract or cytau tes, is a CRF polychoron that has as cells 16 square pyramids, 4 cubes and 4 octahedra.

It can be formed by removing 4 vertices of the icositetrachoron, but can also be formed by augmenting a cycle of four faces of the tesseract with cubic pyramids.

## Vertex coordinates

The vertices of a cyclotetradiminished icositetrachoron of edge length 1 are given by all permutations of the first two coordinates of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\pm {\frac {1}{2}},\pm {\frac {1}{2}},\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm 1,0,0,0\right)}$.

## Representations

A cubic pyramid has the following Coxeter diagrams:

• ox4qo ox4oo&#zx (tegum sum of a tesseract and a 2-edge-length square parallel to one of the tesseract's faces and rotated 45°)
• qoo ooq xox4oqo&#zx
• xox xox4oqo&#xt (cube atop 2-edge-length square rotated 45° atop cube)
• (qo)q(qo) (oo)o(oo)4(ox)x(ox)&#xt