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  2. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    It follows that all vertices are congruent, ... Skilling's figure with overlapping edges. ... 9: 2: Yes: 3: 7{4}+2 ...

  3. Heptahedron - Wikipedia

    en.wikipedia.org/wiki/Heptahedron

    There are 34 topologically distinct convex heptahedra, excluding mirror images. [2] ( Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)

  4. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    In the mathematical field of graph theory, a rhombicosidodecahedral graph is the graph of vertices and edges of the rhombicosidodecahedron, one of the Archimedean solids. It has 60 vertices and 120 edges, and is a quartic graph Archimedean graph. [5] Square centered Schlegel diagram

  5. List of small polyhedra by vertex count - Wikipedia

    en.wikipedia.org/wiki/List_of_small_polyhedra_by...

    The smallest polyhedron is the tetrahedron with 4 triangular faces, 6 edges, and 4 vertices. Named polyhedra primarily come from the families of platonic solids , Archimedean solids , Catalan solids , and Johnson solids , as well as dihedral symmetry families including the pyramids , bipyramids , prisms , antiprisms , and trapezohedrons .

  6. Deltahedron - Wikipedia

    en.wikipedia.org/wiki/Deltahedron

    A non-convex deltahedron is a deltahedron that does not possess convexity, meaning it has neither coplanar faces nor collinear edges. There are infinitely many non-convex deltahedrons. [9] Some examples are stella octangula, the third stellation of a regular icosahedron, and Boerdijk–Coxeter helix. [10] There are subclasses of non-convex ...

  7. Heptagon - Wikipedia

    en.wikipedia.org/wiki/Heptagon

    In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon.. The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.

  8. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    7-cube, Rectified 7-cube, 7-cube, Truncated 7-cube, Cantellated 7-cube, Runcinated 7-cube, Stericated 7-cube, Pentellated 7-cube, Hexicated 7-cube; 7-orthoplex, Rectified 7-orthoplex, Truncated 7-orthoplex, Cantellated 7-orthoplex, Runcinated 7-orthoplex, Stericated 7-orthoplex, Pentellated 7-orthoplex; 1 32 polytope, 2 31 polytope, 3 21 polytope

  9. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    The elements of the set correspond to the vertices, edges, faces and so on of the polytope: vertices have rank 0, edges rank 1, etc. with the partially ordered ranking corresponding to the dimensionality of the geometric elements. The empty set, required by set theory, has a rank of −1 and is sometimes said to correspond to the null polytope.