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
Hemi-dodecahedron a real projective plane. With this embedding, the dual graph is "K" (the complete graph with 6 vertices) --- see hemi-icosahedron. Hemi-dodecahedron A hemi-dodecahedron is an abstract regular polyhedron, containing half the faces of a regular dodecahedron. It can be realized as a projective polyhedron (a tessellation of the real projective plane by 6 pentagons), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected and dividing the hemisphere into three equal parts. It has 6 pentagonal faces, 15 edges, and 10 vertices. It can be projected symmetrically inside of