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  2. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    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.

  3. Goldberg polyhedron - Wikipedia

    en.wikipedia.org/wiki/Goldberg_polyhedron

    They are defined by three properties: each face is either a pentagon or hexagon, exactly three faces meet at each vertex, and they have rotational icosahedral symmetry. They are not necessarily mirror-symmetric; e.g. GP(5,3) and GP(3,5) are enantiomorphs of each other. A Goldberg polyhedron is a dual polyhedron of a geodesic polyhedron.

  4. Rhombic dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedron

    It has 8 vertices adjusted in or out in alternate sets of 4, with the limiting case a tetrahedral envelope. Variations can be parametrized by (a,b), where b and a depend on each other such that the tetrahedron defined by the four vertices of a face has volume zero, i.e. is a planar face. (1,1) is the rhombic solution.

  5. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.

  6. Tetrakis cuboctahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrakis_cuboctahedron

    A cat toy in the shape of a tetrakis cuboctahedron projected onto a sphere Tetrakis cuboctahedrons usefully represent carbon atoms in a 3D ball-and-stick model of a diamond lattice as the normals to alternate yellow-shaded faces in the top image correspond exactly to the tetrahedral bond angles 3D model of a tetrakis cuboctahedron

  7. Face (geometry) - Wikipedia

    en.wikipedia.org/wiki/Face_(geometry)

    The (n − 3)-faces of an n-polytope are called peaks. A peak contains a rotational axis of facets and ridges in a regular polytope or honeycomb. For example: The peaks of a 3D polyhedron or plane tiling are its 0-faces or vertices. The peaks of a 4D polytope or 3-honeycomb are its 1-faces or edges.

  8. Rhombic triacontahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_triacontahedron

    3D model of a rhombic triacontahedron. The rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron

  9. List of Johnson solids - Wikipedia

    en.wikipedia.org/wiki/List_of_Johnson_solids

    A convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors exclude uniform polyhedra from the definition. 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 ...

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