Truncated pentagonal duoprism

Truncated pentagonal duoprism
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Tapedip
Elements
Cells	25 tetragonal disphenoids, 10 truncated pentagonal prisms
Faces	100 isosceles triangles, 25 ditetragons, 10 dipentagons
Edges	50+50+100
Vertices	100
Vertex figure	Sphenoid
Measures (variant with decagon edge length 1)
Edge lengths	Lacing edges (100): $\frac{\sqrt{10}-\sqrt2}{2} ≈ 0.87403$
	Edges of decagons (50+50): 1
Circumradius	$\sqrt{4+\sqrt5} ≈ 2.49721$
Central density	1
Related polytopes
Army	Tapedip
Regiment	Tapedip
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2≀S2, order 200
Convex	Yes
Nature	Tame

The truncated pentagonal duoprism or tapedip is a convex isogonal polychoron that consists of 10 truncated pentagonal prisms and 25 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated pentagonal prisms join at each vertex. It can be formed by truncating the pentagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform pentagonal-decagonal duoprisms chosen such that the decagonal and pentagonal prisms have the same circumradius. if the decagons of this duoprism have edge length 1, the pentagons have edge length $\sqrt5 ≈ 2.23607$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\frac{\sqrt{3+\sqrt5}}{2}$ ≈ 1:1.14412.