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
Tetrated dodecahedron Johnson solid, the four triangles corresponding to the face planes of a tetrahedron are always equilateral, while the pentagons and the other triangles only have reflection symmetry. The 12 pentagons and 16 triangles are colored in this net by their locations within the tetrahedral symmetry. Tetrated dodecahedron The tetrated dodecahedron is a near-miss Johnson solid. It was first discovered in 2002 by Alex Doskey. It was then independently rediscovered in 2003 and named by Robert Austin. It has 28 faces: twelve regular pentagons arranged in four panels of three pentagons each, four equilateral triangles (shown in blue), and six pairs