Ditetragonal prism

Ditetragonal prism
Rank	3
Type	Semi-uniform
Space	Spherical
Notation
Bowers style acronym	Detip
Coxeter diagram	x y4z
Elements
Faces	4+4 rectangles, 2 ditetragons
Edges	8+8+8
Vertices	16
Vertex figure	Scalene triangle
Measures (edge lengths a, b (base), c (sides))
Circumradius	$\sqrt{\frac{a^2+b^2+ab\sqrt2}{2}+\frac{c^2}{4}}$
Volume	$(a^2c+2abc\sqrt2+b^2c)$
Dihedral angles	4–4: 135°
	4–8: 90°
Height	c
Central density	1
Related polytopes
Army	Detip
Regiment	Detip
Dual	Tetrambic tegum
Conjugate	Ditetragrammic prism
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	B2×A1, order 16
Convex	Yes
Nature	Tame

The ditetragonal prism is a prism based on the ditetragon. As such it is a semi-uniform polyhedron with 2 ditetragons and 2 sets of 4 rectangles as faces.

The general ditetragonal prism can be alternated into a square gyroprism.

Vertex coordinates

A ditetragonal prism with base edges of length a and b, and side edges of length c, has vertex coordinates given by all permutations of the first two coordinates of:

• $\left(±\frac{a+b\sqrt2}{2},\,±\frac{a}{2},\,±\frac{c}{2}\right).$