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  2. Isohedral figure - Wikipedia

    en.wikipedia.org/wiki/Isohedral_figure

    Similarly, a k-isohedral tiling has k separate symmetry orbits (it may contain m different face shapes, for m = k, or only for some m < k). [ 6 ] ("1-isohedral" is the same as "isohedral".) A monohedral polyhedron or monohedral tiling ( m = 1) has congruent faces, either directly or reflectively, which occur in one or more symmetry positions.

  3. Icosahedron - Wikipedia

    en.wikipedia.org/wiki/Icosahedron

    Convex regular icosahedron A tensegrity icosahedron. In geometry, an icosahedron (/ ˌ aɪ k ɒ s ə ˈ h iː d r ən,-k ə-,-k oʊ-/ or / aɪ ˌ k ɒ s ə ˈ h iː d r ən / [1]) is a polyhedron with 20 faces.

  4. Triakis icosahedron - Wikipedia

    en.wikipedia.org/wiki/Triakis_icosahedron

    When depicted in Leonardo's form, with equilateral triangle faces, it is an example of a non-convex deltahedron, one of the few known deltahedra that are isohedral (meaning that all faces are symmetric to each other). [4]

  5. Regular icosahedron - Wikipedia

    en.wikipedia.org/wiki/Regular_icosahedron

    The 600-cell has icosahedral cross sections of two sizes, and each of its 120 vertices is an icosahedral pyramid; the icosahedron is the vertex figure of the 600-cell. The unit-radius 600-cell has tetrahedral cells of edge length 1 φ {\textstyle {\frac {1}{\varphi }}} , 20 of which meet at each vertex to form an icosahedral pyramid (a 4 ...

  6. List of isotoxal polyhedra and tilings - Wikipedia

    en.wikipedia.org/wiki/List_of_isotoxal_polyhedra...

    In geometry, isotoxal polyhedra and tilings are defined by the property that they have symmetries taking any edge to any other edge. [1] Polyhedra with this property can also be called "edge-transitive", but they should be distinguished from edge-transitive graphs, where the symmetries are combinatorial rather than geometric.

  7. Solids with icosahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Solids_with_icosahedral...

    Solids with full icosahedral symmetry. Platonic solids - regular polyhedra (all faces of the same type) {5,3} {3,5}

  8. Catalan solid - Wikipedia

    en.wikipedia.org/wiki/Catalan_solid

    Each Catalan solid has constant dihedral angles, meaning the angle between any two adjacent faces is the same. [1] Additionally, two Catalan solids, the rhombic dodecahedron and rhombic triacontahedron, are edge-transitive, meaning their edges are symmetric to each other.

  9. Truncated icosahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_icosahedron

    The truncated icosahedron 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. [5] It has the same symmetry as the regular icosahedron, the icosahedral symmetry, and it also has the property of vertex-transitivity.