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  2. List of regular polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_regular_polytopes

    12 3-dimensional "pure" apeirohedra based on the structure of the cubic honeycomb, {4,3,4}. [22] A π petrie dual operator replaces faces with petrie polygons; δ is a dual operator reverses vertices and faces; φ k is a kth facetting operator; η is a halving operator, and σ skewing halving operator.

  3. Archimedean solid - Wikipedia

    en.wikipedia.org/wiki/Archimedean_solid

    The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygons, but not all alike, and whose vertices are all symmetric to each other. The solids were named after Archimedes, although he did not claim credit for them. They belong to the class of uniform polyhedra, the polyhedra with regular faces and symmetric ...

  4. Geodesic polyhedron - Wikipedia

    en.wikipedia.org/wiki/Geodesic_polyhedron

    In Magnus Wenninger's Spherical models, polyhedra are given geodesic notation in the form {3,q+} b,c, where {3,q} is the Schläfli symbol for the regular polyhedron with triangular faces, and q-valence vertices. The + symbol indicates the valence of the vertices being increased. b,c represent a subdivision description, with 1,0 representing the ...

  5. Polytope - Wikipedia

    en.wikipedia.org/wiki/Polytope

    These bounding sub-polytopes may be referred to as faces, or specifically j-dimensional faces or j-faces. A 0-dimensional face is called a vertex, and consists of a single point. A 1-dimensional face is called an edge, and consists of a line segment. A 2-dimensional face consists of a polygon, and a 3-dimensional face, sometimes called a cell ...

  6. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    Nevertheless, there is general agreement that a polyhedron is a solid or surface that can be described by its vertices (corner points), edges (line segments connecting certain pairs of vertices), faces (two-dimensional polygons), and that it sometimes can be said to have a particular three-dimensional interior volume.

  7. List of two-dimensional geometric shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_two-dimensional...

    This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.

  8. Regular polyhedron - Wikipedia

    en.wikipedia.org/wiki/Regular_polyhedron

    All these lunes share two common vertices. [13] A regular dihedron, {n, 2} [13] (2-hedron) in three-dimensional Euclidean space can be considered a degenerate prism consisting of two (planar) n-sided polygons connected "back-to-back", so that the resulting object has no depth, analogously to how a digon can be constructed with two line segments.

  9. Regular polytope - Wikipedia

    en.wikipedia.org/wiki/Regular_polytope

    In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.