Blended tetrahedron

Blended tetrahedron
Rank	3
Type	Regular
Space	4D Euclidean space
Notation
Schläfli symbol	$\{3,3\}\#\{\}$ $\{6,3\}_{(2,0)}$ $\{6,3\}_4$
Elements
Faces	4 skew triangles
Edges	12
Vertices	8
Related polytopes
Army	Tepe
Convex hull	Tetrahedral prism
Abstract & topological properties
Flag count	48
Euler characteristic	0
Schläfli type	{6,3}
Orientable	Yes
Genus	1
Properties
Symmetry	A3×A1, order 48
Convex	No

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:

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

Related polytopes

The blended tetrahedron is abstractly equivalent to the Petrial cube.

External links

• Hartley, Michael. "{6,3}*48".