Small snub icosicosidodecahedron = (1+)/2 is the golden ratio and α = . Small snub icosicosidodecahedron In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron. It also called a holosnub icosahedron, ß{3,5}. The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries. Its convex hull is a nonuniform truncated icosahedron. Cartesian coordinates for the vertices of a small
Regular dodecahedron Shown here including the inner 12 vertices, which are not connected by the outer hull edges of 6D norm length , form a regular icosahedron. <br>The 3D projection basis vectors ["u","v","w"] used are: Regular dodecahedral objects have found some practical applications, and have also played a role in the visual arts and in philosophy. Iamblichus states that Hippasus, a Pythagorean, perished in the sea, because he boasted that he first divulged "the sphere with the twelve pentagons." In "Theaetetus", a dialogue of Plato, Plato was able to prove that there are just five uniform regular solids; these later became known