Ditrigonal trapezoprism

Ditrigonal trapezoprism
Rank	3
Type	Isogonal
Notation
Bowers style acronym	Dittra
Coxeter diagram	s s6x ()
Elements
Faces	6 isosceles trapezoids 2 ditrigons
Edges	6+6+6
Vertices	12
Vertex figure	Scalene triangle
Measures (edge lengths a, b (base), c (lacing))
Circumradius	${\frac {\sqrt {(a+b)^{2}+c^{2}}}{2}}$
Height	${\sqrt {c^{2}-{\frac {(b-a)^{2}}{3}}}}$
Central density	1
Related polytopes
Army	Dittra
Regiment	Dittra
Dual	Triangular scalenohedron
Conjugate	Ditrigonal trapezoprism
Abstract & topological properties
Flag count	72
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	(G2×A1)/2, order 12
Flag orbits	6
Convex	Yes
Nature	Tame

The ditrigonal trapezoprism is a variant of the hexagonal prism with triangular antiprism symmetry. It is isogonal, with 2 ditrigons as bases connected by 6 isosceles trapezoids.

A version with ditrigons of side lengths 1 and $1+{\sqrt {3}}$ and lacing edges of length ${\sqrt {2}}$ occurs as an edge-alternation of the uniform dodecagonal prism.

External links

• Klitzing, Richard. "ditriangular trapezoprism".