Digonal-triangular truncatoprismantiprismoid

Digonal-triangular truncatoprismantiprismoid
File:Digonal-triangular truncatoprismantiprismoid.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	12 rectangular frustums, 6 cuboids, 6 rectangular trapezoprisms, 4 ditrigonal prisms, 4 ditrigonal trapezoprisms
Faces	24+24 isosceles trapezoids, 12+12+12+12 rectangles, 8 ditrigons
Edges	24+24+24+24+24
Vertices	48
Vertex figure	Irregular triangular tegum
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Digonal-triangular apiculatotegmantitegmoid
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	(B2×G2)/2, order 48
Convex	Yes
Nature	Tame

The digonal-triangular truncatoprismantiprismoid is a convex isogonal polychoron that consists of 4 ditrigonal prisms, 4 ditrigonal trapezoprisms, 6 cuboids, 6 rectangular trapezoprisms, and 12 rectangular frustums. 2 rectangular frustums and one of each of the other cell types join at each vertex. It can be formed as a convex hull of two rectangular-ditrigonal duoprisms. However, it cannot be made uniform.

This polychoron can be alternated into a snub digonal-triangular prismantiprismoid, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\frac {5+{\sqrt {30}}}{5}}$ ≈ 1:2.09545.

Vertex coordinates

The vertices of a digonal-triangular truncatoprismantiprismoid, assuming that the edge length differences are minimized, centered at the origin, are given as Cartesian products of the vertices of ditrigon DT₁ and rectangle R₁, both of lengths 1 and ${\frac {5+{\sqrt {30}}}{5}}$:

• DT₁ × R₁,
• DT₂ × R₂ (DT₁ rotated 60 degrees and R₁ rotated 90 degrees).