# Pentagonal tetraswirlprism

Pentagonal tetraswirlprism
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells200 phyllic disphenoids, 100 rhombic disphenoids, 40 pentagonal gyroprisms
Faces400+400 scalene triangles, 40 pentagons
Edges100+100+200+200
Vertices100
Vertex figure12-vertex polyhedron with 4 tetragons and 12 triangles
Measures (based on pentagonal duoprisms of edge length 1)
Edge lengthsShort 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 density1
Related polytopes
DualPentagonal tetraswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(20)≀S2)+/4, order 400
ConvexYes
NatureTame

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.