# Blended tetrahedron

Blended tetrahedron
Rank3
Dimension4
TypeRegular
Notation
Schläfli symbol${\displaystyle \{3,3\}\#\{\}}$
${\displaystyle \{6,3\}_{(2,0)}}$
${\displaystyle \{6,3\}_{4}}$
Elements
Faces4 skew triangles
Edges12
Vertices8
Petrie polygons6 skew squares
Related polytopes
ArmyTepe
Petrie dualBlended Petrial tetrahedron
Convex hullTetrahedral prism
Abstract & topological properties
Flag count48
Euler characteristic0
Schläfli type{6,3}
OrientableYes
Genus1
Properties
SymmetryA3×A1, order 48
ConvexNo
Dimension vector(2,3,3)

The blended tetrahedron or skew tetrahedron is a regular skew polyhedron in 4D Euclidean space. It is the result of blending a tetrahedron with a dyad.

## Vertex coordinates

The vertex coordinates for the blended tetrahedron of unit edge length and skew distance can be given by all permutations of:

• ${\displaystyle \left(\pm {\dfrac {\sqrt {2}}{2}},\,0,\,0,\,0\right)}$.

## Related polytopes

The blended tetrahedron is abstractly equivalent to the Petrial cube.

In four dimensions, it is the kappa of the tetrahedron.