Medial inverted pentagonal hexecontahedron

From Polytope Wiki
Jump to navigation Jump to search
Medial inverted pentagonal hexecontahedron
DU60 medial inverted pentagonal hexecontahedron.png
TypeUniform dual
Coxeter diagramp5/3p5p (CDel node fh.pngCDel 5.pngCDel rat.pngCDel 3x.pngCDel node fh.pngCDel 5.pngCDel node fh.png)
Faces60 irregular pentagons
Vertex figure60 triangles, 12 pentagons, 12 pentagrams
Measures (edge length 1)
Inradius≈ 0.55808
Dihedral angle≈ 108.09572°
Central density9
Number of pieces60
Related polytopes
DualInverted snub dodecadodecahedron
Abstract properties
Flag count600
Euler characteristic–6
Topological properties
SymmetryH3+, order 60

The medial inverted pentagonal hexecontahedron is a uniform dual polyhedron. It consists of 60 irregular pentagons, each with two short, one medium, and two long edges. Its dual is the inverted snub dodecadodecahedron.

If the pentagon faces have medium edge length 2, then the short edge length is , and the long edge length is , where is the largest (least negative) real root of the polynomial . ​​The pentagons have three interior angles of , one of , and one of , where is the golden ratio.

A dihedral angle can be given as .

The inradius R ≈ 0.55808 of the medial inverted pentagonal hexecontahedron with unit edge length is equal to the square root of a real root of .

External links[edit | edit source]