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  2. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set.

  3. Facet (geometry) - Wikipedia

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

    In three-dimensional geometry, a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face. [ 1 ] [ 2 ] To facet a polyhedron is to find and join such facets to form the faces of a new polyhedron; this is the reciprocal process to stellation and may also be applied to higher-dimensional polytopes .

  4. Polytope - Wikipedia

    en.wikipedia.org/wiki/Polytope

    In certain fields of mathematics, the terms "polytope" and "polyhedron" are used in a different sense: a polyhedron is the generic object in any dimension (referred to as polytope in this article) and polytope means a bounded polyhedron. [6] This terminology is typically confined to polytopes and polyhedra that are convex.

  5. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.

  6. Isogonal figure - Wikipedia

    en.wikipedia.org/wiki/Isogonal_figure

    In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.

  7. Uniform polyhedron - Wikipedia

    en.wikipedia.org/wiki/Uniform_polyhedron

    In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent . Uniform polyhedra may be regular (if also face- and edge-transitive ), quasi-regular (if also edge-transitive but not face-transitive), or semi-regular ...

  8. List of polygons, polyhedra and polytopes - Wikipedia

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

    Regular polyhedron. Platonic solid: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot polyhedron (Regular star polyhedra) Small stellated dodecahedron, Great stellated dodecahedron, Great icosahedron, Great dodecahedron; Abstract regular polyhedra (Projective polyhedron)

  9. N-dimensional polyhedron - Wikipedia

    en.wikipedia.org/wiki/N-dimensional_polyhedron

    Many traditional polyhedral forms are n-dimensional polyhedra. Other examples include: A half-space is a polyhedron defined by a single linear inequality, a 1 T x ≤ b 1. A hyperplane is a polyhedron defined by two inequalities, a 1 T x ≤ b 1 and a 1 T x ≥ b 1 (which is equivalent to -a 1 T x ≤ -b 1). A quadrant in the plane.