Divide the vertices of this polyhedron into two groups:
- Group A consisting of vertices, which are common points of 3 edges.
- Group B consisting of vertices, which are common points of 5 edges.
It appears that points of the group A – these are vertices of some regular dodecahedron.
It appears also that points of the group B – these are vertices of some regular icosahedron.
(Notice: both dodecahedron and icosahedron are Plato's polyhedrons.
See a page of ‘Literka’ about them.)
It follows that all vertices lie on some 2 spheres.
This polyhedron could be obtained in the following way: take a regular dodecahedron, take a plane H joining and edge with a symmetry center,
draw a plane perpendicular to this plane H passing through this edge; finally do this with all edges: as a result we obtain 30-faces polyhedron
built of rhombuses.
