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
Diminished rhombic dodecahedron a cuboctahedron. It retains 5 square faces, and 4 equilateral triangle faces of the cuboctahedron. The 13 Cartesian coordinate can be positioned as: Augmenting two opposite squares will create a dihedral rhombic dodecahedron, doubling the symmetry to "D" symmetry, order 16. Augmenting pyramids on all six square faces, with merged faces will produce a regular octahedron, restoring full octahedral symmetry, order 48. Diminished rhombic dodecahedron In geometry, a diminished rhombic dodecahedron is a rhombic dodecahedron with one or more vertices removed. This article describes diminishing one 4-valence vertex. This diminishment creates one new square face while 4 rhombic faces are