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
First stellation of rhombic dodecahedron First stellation of rhombic dodecahedron In geometry, the first stellation of the rhombic dodecahedron is a stellation of the rhombic dodecahedron. This polyhedron is sometimes called "Escher's solid"; it appears in M. C. Escher's works "Waterfall" and in a study for "Stars" (although "Stars" itself features a different shape, the compound of three octahedra). It has 48 faces, all triangles. It has 26 vertices in total: 6 with degree 8, 8 with degree 6, and 12 with degree 4. It has 72 edges in total, giving an Euler characteristic of 26 + 48 − 72 = +2. Its vertices are