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  2. Pentakis dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Pentakis_dodecahedron

    Let be the golden ratio.The 12 points given by (,,) and cyclic permutations of these coordinates are the vertices of a regular icosahedron.Its dual regular dodecahedron, whose edges intersect those of the icosahedron at right angles, has as vertices the points (,,) together with the points (, /,) and cyclic permutations of these coordinates.

  3. Pentakis icosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Pentakis_icosidodecahedron

    Pentakis dodecahedron is a slightly smaller Catalan solid which has 60 isosceles triangle faces, 90 edges (2 types), and 32 vertices (2 types). Tripentakis icosidodecahedron, the Kleetope of the icosidodecahedron, can be obtained by raising low pyramids on each equilateral triangular face on a pentakis icosidodecahedron.

  4. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    Printable version; In other projects ... 15 as representatives of the infinite families of ... ⁠ 5 / 3 ⁠ (3) ⁠ 5 / 2 ⁠ have some faces occurring as ...

  5. List of polygons, polyhedra and polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_polygons...

    Vertex the (n−5)-face of the 5-polytope; Edge the (n−4)-face of the 5-polytope; Face the peak or (n−3)-face of the 5-polytope; Cell the ridge or (n−2)-face of the 5-polytope; Hypercell or Teron the facet or (n−1)-face of the 5-polytope

  6. Truncation (geometry) - Wikipedia

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

    Faces are reduced to half as many sides, and square faces degenerate into edges. For example, the tetrahedron is an alternated cube, h{4,3}. Diminishment is a more general term used in reference to Johnson solids for the removal of one or more vertices, edges, or faces of a polytope, without disturbing the other vertices.

  7. Snub dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Snub_dodecahedron

    The snub dodecahedron can be generated by taking the twelve pentagonal faces of the dodecahedron and pulling them outward so they no longer touch. At a proper distance this can create the rhombicosidodecahedron by filling in square faces between the divided edges and triangle faces between the divided vertices. But for the snub form, pull the ...

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  9. Vertex configuration - Wikipedia

    en.wikipedia.org/wiki/Vertex_configuration

    A vertex configuration can also be represented as a polygonal vertex figure showing the faces around the vertex. This vertex figure has a 3-dimensional structure since the faces are not in the same plane for polyhedra, but for vertex-uniform polyhedra all the neighboring vertices are in the same plane and so this plane projection can be used to visually represent the vertex configuration.

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