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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.
Pages in category "Archimedean solids" The following 15 pages are in this category, out of 15 total. This list may not reflect recent changes. ...
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.
3.2 Archimedean solids. 3.3 Prisms and antiprisms. 3.4 Catalan solids. 3.5 Bipyramids and Trapezohedron. 3.6 Uniform star polyhedra. 3.7 Uniform prismatic star polyhedra.
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 a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices, and 120 edges.
The dual of a regular polyhedron is regular, while the dual of an Archimedean solid is a Catalan solid. The concept of uniform polyhedron is a special case of the concept of uniform polytope, which also applies to shapes in higher-dimensional (or lower-dimensional) space.
A uniform polyhedron is a polyhedron in which the faces are regular and they are isogonal; examples include Platonic and Archimedean solids as well as prisms and antiprisms. [4] The Johnson solids are named after American mathematician Norman Johnson (1930–2017), who published a list of 92
The Archimedean solids are the class of thirteen polyhedra whose faces are all regular polygons and whose vertices are symmetric to each other; [c] their dual polyhedra are Catalan solids. [50] The class of regular polygonal faces polyhedron are the deltahedron (whose faces are all equilateral triangles and Johnson solids (whose faces are ...