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In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces. The snub dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equilateral triangles .
In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U 40. It has 84 faces (60 triangles , 12 pentagons , and 12 pentagrams ), 150 edges, and 60 vertices. [ 1 ] It is given a Schläfli symbol sr{ 5 ⁄ 2 ,5}, as a snub great dodecahedron .
Of all vertex-transitive polyhedra, it occupies the largest percentage (89.80%) of the volume of a sphere in which it is inscribed, very narrowly beating the snub dodecahedron (89.63%) and small rhombicosidodecahedron (89.23%), and less narrowly beating the truncated icosahedron (86.74%); it also has by far the greatest volume (206.8 cubic ...
Truncated dodecahedron: 3.10.10: 20 triangles 12 decagons: 90 60 I h: Truncated icosahedron: 5.6.6: 12 pentagons 20 hexagons 90 60 I h: Rhombicosidodecahedron: 3.4.5.4: 20 triangles 30 squares 12 pentagons 120 60 I h: Truncated icosidodecahedron: 4.6.10: 30 squares 20 hexagons 12 decagons 180 120 I h: Snub dodecahedron: 3.3.3.3.5: 80 triangles ...
The snub disphenoid name comes from Johnson (1966) classification of the Johnson solid. [12] However, this solid was first studied by Rausenberger (1915). [13] [14] It was studied again in the paper by Freudenthal & van d. Waerden (1947), which first described the set of eight convex deltahedra, and named it the Siamese dodecahedron. [15] [14]
It is explicitly called a pentatruncated pentagonal hexecontahedron since only the valence-5 vertices of the pentagonal hexecontahedron are truncated. [2]Its topology can be constructed in Conway polyhedron notation as t5gD and more simply wD as a whirled dodecahedron, reducing original pentagonal faces and adding 5 distorted hexagons around each, in clockwise or counter-clockwise forms.
Net (click to enlarge) The pentakis snub dodecahedron is a convex polyhedron with 140 triangular faces, 210 edges, and 72 vertices. It has chiral icosahedral symmetry ...
3D model of a snub icosidodecadodecahedron. In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U 46. It has 104 faces (80 triangles, 12 pentagons, and 12 pentagrams), 180 edges, and 60 vertices. [1] As the name indicates, it belongs to the family of snub polyhedra.