In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (icosi-) triangular faces and twelve (dodeca-) pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon.

"The" (quasiregular) icosidodecahedron is the 32-faced Archimedean solid with faces 20{3}+12{5}. It is one of the two convex quasiregular polyhedra. It is illustrated above together with a wireframe version and a net that can be used for its construction.

In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U 54. It has 32 faces (20 triangles and 12 pentagrams ), 60 edges, and 30 vertices. [ 1 ] It is given a Schläfli symbol r{3, 5 ⁄ 2 }.

An icosidodecahedron is a polyhedron (a three-dimensional shape) with 20 (icosi) triangular faces and 12 (dodeca) pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon.

An IcosiDodecahedron is the intersection of an icosahedron and a dodecahedron if these two are scaled so that their corresponding edges intersect at their midpoints. See the following animation. The IcosiDodecahedron is obtained in the same way by midpoint truncation from the dodecahedron or from the icosahedron.

The icosidodecahedron can be built by truncating either a regular icosahedron or a regular do-decahedron. It has 30 vertices, one at the center of each edge of the icosahedron—or equivalently, one at the center of each edge of a dodecahedron. It is a beautiful, highly symmetrical shape.

Properties of the icosidodecahedron: Number of faces, edges and dihedral angle measure. The icosidodecahedron is created by either truncating (cutting off) the dodecahedron one half of the way into each side or truncating the icosahedron one half of the way into each side. 60 edges. Dihedral angles: 142 degrees, 37 minutes.

The icosidodecahedron is a semiregular convex polyhedron with two properties: 1. All faces are regular polygons of two types - a pentagon and a triangle; 2. For any pair of vertices, there is a symmetry of the polyhedron (that is, a motion that translates the polyhedron into itself) that transforms one vertex to another.

2023年2月23日 · The icosidodecahedron is a complex three-dimensional solid that serves as the full-edge truncation between two regular solids: the dodecahedron and the icosahedron. It is an extraordinary example of a quasiregular polyhedron, which exists in a sequence of symmetries progressing from tilings of the sphere to the Euclidean and hyperbolic planes.

If, when truncating the vertices of either the icosahedron or the dodecahedron, we move in exactly half way, the result is the icosidodecahedron. Thus, we can think of the icosidodecahedron as being the limiting case of either the truncated icosahedron or the truncated dodecahedron.