Hexeractidiminished rectified hexacontatetrapeton

Hexeractidiminished rectified hexacontatetrapeton
File:Hexeractidiminished rectified hexacontatetrapeton.png (OFF file)
Rank	6
Type	Scaliform
Notation
Bowers style acronym	Xedrag
Coxeter diagram	xxo4ooo xox4ooo oxx4ooo&#zx
Elements
Peta	64 tridiminished rectified hexatera, 12 hexadecachoric prisms
Tera	192 tetrahedral prisms, 192 bidiminished rectified pentachora, 12 hexadecachora
Cells	192 tetrahedra, 192 square pyramids, 384 triangular prisms
Faces	64+384 triangles, 48+192 squares
Edges	96+192
Vertices	48
Vertex figure	Tetradiminished hexadecachoric prism
Measures (edge length 1)
Circumradius	1
Central density	1
Related polytopes
Dual	Hexeractistellated joined hexacontatetrapeton
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2≀S3, order 3072
Convex	Yes
Nature	Tame

The hexeractidiminished rectified hexacontatetrapeton or xedrag, also known as the square cuboctahedrotriate, is a convex scaliform polypeton that consists of 12 hexadecachoric prisms and 64 tridiminished rectified hexatera formed from deleting the vertices of a hexacontatetrapeton (considered as a square triotegum) from a rectified hexacontatetrapeton.

It was discovered on March 2, 2021.

Vertex coordinates

The vertices of a hexeractidiminished rectified hexacontatetrapeton of edge length 1 are given by:

${\biggl (}0,0,\pm {\frac {1}{2}},\pm {\frac {1}{2}},\pm {\frac {1}{2}},\pm {\frac {1}{2}}{\biggr )}$

${\biggl (}\pm {\frac {1}{2}},\pm {\frac {1}{2}},0,0,\pm {\frac {1}{2}},\pm {\frac {1}{2}}{\biggr )}$

${\biggl (}\pm {\frac {1}{2}},\pm {\frac {1}{2}},\pm {\frac {1}{2}},\pm {\frac {1}{2}},0,0{\biggr )}$

These coordinates show that a hexeractidiminished rectified hexacontatetrapeton can be obtained as the convex hull of three triorthoaligned tesseracts.

Externall inks

• Klitzing, Richard. "xedrag".