Hexapentakis truncated icosahedron constructed as an augmented truncated icosahedron, adding pyramids to the 20 hexagonal faces, creating 120 new triangular faces. It is visually similar to the chiral snub dodecahedron which has 80 triangles and 12 pentagons. The dual polyhedron can be seen as a "hexatruncated pentakis dodecahedron", a dodecahedron with its faced augmented by pentagonal pyramids (a pentakis dodecahedron), and then its 6-valance vertices truncated. It has similar groups of irregular pentagons as the pentagonal hexecontahedron. Hexapentakis truncated icosahedron The hexapentakis truncated icosahedron is a convex polyhedron constructed as an augmented truncated icosahedron. It is geodesic polyhedron {3,5+}, with pentavalent vertices separated
Snub dodecahedron of snubbed polyhedra and tilings with vertex figure (3.3.3.3."n") and Coxeter–Dynkin diagram . These figures and their duals have ("n"32) rotational symmetry, being in the Euclidean plane for "n" = 6, and hyperbolic plane for any higher "n". The series can be considered to begin with "n" = 2, with one set of faces degenerated into digons. In the mathematical field of graph theory, a snub dodecahedral graph is the graph of vertices and edges of the snub dodecahedron, one of the Archimedean solids. It has 60 vertices and 150 edges, and is an Archimedean graph. Snub dodecahedron In geometry,