Pentagonal icositetrahedron
The Pentagonikositetraeder is a chiral polyhedron composed of 24 irregular pentagons and one of the the Catalan bodies. It is dual to the beveled hexahedron and has 38 vertices and 60 edges.
The following pictures show two mirror -image Pentagonikositetraeder.
Mirror variant 2
Formation
By connecting the midpoints of five edges that collide in each room of the chamfered corner hexahedron, creates a Sehnenfünfeck whose radius of inscribed circle Tangentenfünfecks, the boundary surface of the Pentagonikositetraeders, is at the same time. In this particular type, all dihedral angles of equal size ( ≈ 136 ° ), and there is a uniform sphere radius edges.
Hereinafter the term designates the cosine of the smaller central angle in the aforementioned Sehnenfünfeck.
Is the edge length of the chamfered hexahedron, the resulting lengths of the sides are represented by Tangentenfünfecks
It follows:
Related polyhedra
Inscribed cube
Inscribed octahedron