Pentagonal tetraswirlprism

Pentagonal tetraswirlprism
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	200 phyllic disphenoids, 100 rhombic disphenoids, 40 pentagonal gyroprisms
Faces	400+400 scalene triangles, 40 pentagons
Edges	100+100+200+200
Vertices	100
Vertex figure	12-vertex polyhedron with 4 tetragons and 12 triangles
Measures (based on pentagonal duoprisms of edge length 1)
Edge lengths	Short side edges (100): $\sqrt{\frac{5+2\sqrt5}{5}}-1 ≈ 0.37638$
	Medium side edges (100): $\sqrt{\frac{5-\sqrt5}{5}} ≈ 0.74350$
	Long side edges (200): $\sqrt{\frac{20+4\sqrt5-\sqrt{250+110\sqrt5}}{10}} ≈ 0.81694$
	Edges of pentagons (200): 1
Circumradius	$\sqrt{\frac{5+\sqrt5}{5}} ≈ 1.20300$
Central density	1
Related polytopes
Dual	Pentagonal tetraswirltegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	(I2(20)≀S2)+/4, order 400
Convex	Yes
Nature	Tame

The pentagonal tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 40 pentagonal gyroprisms, 100 rhombic disphenoids, and 200 phyllic disphenoids. 4 pentagonal gyroprisms, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the icosagonal duoprism. It is the fourth in an infinite family of isogonal pentagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:$\frac{\sqrt5+\sqrt{5+2\sqrt5}}{2}$ ≈ 1:2.65688.