# Pentagonal triswirlprism

Pentagonal triswirlprism
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells150 phyllic disphenoids, 30 pentagonal gyroprisms
Faces300 scalene triangles, 150 isosceles triangles, 30 pentagons
Edges75+150+150
Vertices75
Vertex figure10-vertex polyhedron with 4 tetragons and 8 triangles
Measures (based on pentagonal duoprisms of edge length 1)
Edge lengthsShort side edges (75): $\sqrt{\frac{15+\sqrt5-\sqrt{150+30\sqrt5}}{10}} ≈ 0.50024$ Long side edges (150): $\sqrt{\frac{35+7\sqrt5-\sqrt{750+330\sqrt5}}{20}} ≈ 0.77715$ Edges of pentagons (150): 1
Circumradius$\sqrt{\frac{5+\sqrt5}{5}} ≈ 1.20300$ Central density1
Related polytopes
DualPentagonal triswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(15)≀S2)+/3, order 300
ConvexYes
NatureTame

The pentagonal triswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 30 pentagonal gyroprisms and 150 phyllic disphenoids. 4 pentagonal gyroprisms and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the pentadecagonal duoprism. It is the third in an infinite family of isogonal pentagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:$\frac{\sqrt{30+2\sqrt5+2\sqrt{150+30\sqrt5}}}{4}$ ≈ 1:1.99906.