Truncated decagonal duoprism

Truncated decagonal duoprism
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Tadedip
Elements
Cells	100 tetragonal disphenoids, 20 truncated decagonal prisms
Faces	400 isosceles triangles, 100 ditetragons, 20 didecagons
Edges	200+200+400
Vertices	400
Vertex figure	Sphenoid
Measures (variant with icosagon edge length 1)
Edge lengths	Lacing edges (400): $\sqrt{\frac{5-\sqrt5}{5}} ≈ 0.74350$
	Edges of icosagons (200+200): 1
Circumradius	$\sqrt{\frac{65+19\sqrt5+\sqrt{5650+2390\sqrt5}}{10}} ≈ 4.60802$
Central density	1
Related polytopes
Army	Tadedip
Regiment	Tadedip
Dual	Tetrakis decagonal duotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(10)≀S2, order 800
Convex	Yes
Nature	Tame

The truncated decagonal duoprism or tadedip is a convex isogonal polychoron that consists of 20 truncated decagonal prisms and 100 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated decagonal prisms join at each vertex. It can be formed by truncating the decagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform decagonal-icosagonal duoprisms chosen such that the icosagonal and decagonal prisms have the same circumradius. if the icosagons of this duoprism have edge length 1, the decagons have edge length $1+\sqrt{\frac{10-2\sqrt5}{5}} ≈ 2.05136$.

Using the ratio method, the lowest poossible ratio between the longest and shortest edges is 1:$\frac{\sqrt{5+\sqrt5}}{2}$ ≈ 1:1.34500.