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  2. Polyhedral group - Wikipedia

    en.wikipedia.org/wiki/Polyhedral_group

    The tetrahedral group of order 12, rotational symmetry group of the regular tetrahedron. It is isomorphic to A 4. The conjugacy classes of T are: identity; 4 × rotation by 120°, order 3, cw; 4 × rotation by 120°, order 3, ccw; 3 × rotation by 180°, order 2; The octahedral group of order 24, rotational symmetry group of the cube and the ...

  3. List of Wenninger polyhedron models - Wikipedia

    en.wikipedia.org/wiki/List_of_Wenninger...

    This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger.. The book was written as a guide book to building polyhedra as physical models.

  4. Geodesic polyhedron - Wikipedia

    en.wikipedia.org/wiki/Geodesic_polyhedron

    The primary face of the subdivision is called a principal polyhedral triangle (PPT) or the breakdown structure. Calculating a single PPT allows the entire figure to be created. The frequency of a geodesic polyhedron is defined by the sum of ν = b + c. A harmonic is a subfrequency and can be any whole divisor of ν.

  5. Goldberg polyhedron - Wikipedia

    en.wikipedia.org/wiki/Goldberg_polyhedron

    A similar technique can be applied to construct polyhedra with tetrahedral symmetry and octahedral symmetry. These polyhedra will have triangles or squares rather than pentagons. These variations are given Roman numeral subscripts denoting the number of sides on the non-hexagon faces: GP III (n,m), GP IV (n,m), and GP V (n,m).

  6. Regular polyhedron - Wikipedia

    en.wikipedia.org/wiki/Regular_polyhedron

    All five have C 2 ×S 5 symmetry but can only be realised with half the symmetry, that is C 2 ×A 5 or icosahedral symmetry. [9] [10] [11] They are all topologically equivalent to toroids. Their construction, by arranging n faces around each vertex, can be repeated indefinitely as tilings of the hyperbolic plane. In the diagrams below, the ...

  7. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    [K] Kaleido, 1993: The 80 figures were grouped by symmetry: 1–5 as representatives of the infinite families of prismatic forms with dihedral symmetry, 6–9 with tetrahedral symmetry, 10–26 with octahedral symmetry, 27–80 with icosahedral symmetry.

  8. Uniform polyhedron - Wikipedia

    en.wikipedia.org/wiki/Uniform_polyhedron

    Coxeter, Longuet-Higgins & Miller (1954) define uniform polyhedra to be vertex-transitive polyhedra with regular faces. They define a polyhedron to be a finite set of polygons such that each side of a polygon is a side of just one other polygon, such that no non-empty proper subset of the polygons has the same property.

  9. Template:Polyhedron types - Wikipedia

    en.wikipedia.org/wiki/Template:Polyhedron_types

    Polyhedral compounds Deltahedra (Deltahedra, equilateral triangle faces) Snub polyhedra (12 uniform, not mirror image) Zonohedron (Zonohedra, faces have 180°symmetry) Dual polyhedron: Self-dual polyhedron Catalan solid (13, Archimedean dual)

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