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Some Archimedean solids were portrayed in the works of artists and mathematicians during the Renaissance. The elongated square gyrobicupola or pseudorhombicuboctahedron is an extra polyhedron with regular faces and congruent vertices, but it is not generally counted as an Archimedean solid because it is not vertex-transitive.
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
The thirteen Archimedean solids. The elongated square gyrobicupola (also called a pseudo-rhombicuboctahedron), a Johnson solid, has identical vertex figures (3.4.4.4) but because of a twist it is not vertex-transitive. Branko Grünbaum argued for including it as a 14th Archimedean solid. An infinite series of convex prisms.
In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, [1] great rhombicosidodecahedron, [2] [3] omnitruncated dodecahedron or omnitruncated icosahedron [4] is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.
There are two traditional methods for making polyhedra out of paper: polyhedral nets and modular origami.In the net method, the faces of the polyhedron are placed to form an irregular shape on a flat sheet of paper, with some of these faces connected to each other within this shape; it is cut out and folded into the shape of the polyhedron, and the remaining pairs of faces are attached together.
In geometry, the Waterman polyhedra are a family of polyhedra discovered around 1990 by the mathematician Steve Waterman.A Waterman polyhedron is created by packing spheres according to the cubic close(st) packing (CCP), also known as the face-centered cubic (fcc) packing, then sweeping away the spheres that are farther from the center than a defined radius, [1] then creating the convex hull ...
The rhombicuboctahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. [14] The polygonal faces that meet for every vertex are one equilateral triangle and three squares, and the vertex figure is denoted as 3 ⋅ 4 3 {\displaystyle 3\cdot ...
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular ), 36 edges, and 24 vertices. If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and δ S +1 , where δ S is the silver ratio, √ 2 +1.