Alternative tesseract

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Alternative tesseract
Rank4
Dimension4
TypeRegular
Notation
Schläfli symbol
Elements
Cells8 blended Petrial tetrahedra
Faces24 skew squares
Edges32
Vertices16
Vertex figureTetrahedron
Petrie polygons24 octagrammic-square coils
Related polytopes
Petrie dualPetrial alternative tesseract
Convex hullTesseract
Abstract & topological properties
Flag count384
Euler characteristic0
Schläfli type{4,3,3}
OrientableYes
SkeletonQ 4 
Properties
SymmetryB4, order 384
ConvexNo
Dimension vector(1,3,3,3)

The alternative tesseract (also called the alternative 4-cube) is a regular skew polychoron. It is abstractly equivalent to the tesseract. It can be constructed as the kappa of the tesseract.

Vertex coordinates[edit | edit source]

Vertex coordinates for an alternative tesseract of unit edge length can be given as:

  • .