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A regular icosahedron can be distorted or marked up as a lower pyritohedral symmetry, [2] [3] and is called a snub octahedron, snub tetratetrahedron, snub tetrahedron, and pseudo-icosahedron. [4] This can be seen as an alternated truncated octahedron .
A crossed prism is a nonconvex polyhedron constructed from a prism, where the vertices of one base are inverted around the center of this base (or rotated by 180°). This transforms the side rectangular faces into crossed rectangles. For a regular polygon base, the appearance is an n-gonal hour glass. All oblique edges pass through a single ...
A polyhedron with only equilateral triangles as faces is called a deltahedron. There are only eight different convex deltahedra, one of which is the regular icosahedron. [4] The regular icosahedron can also be constructed starting from a regular octahedron. All triangular faces of a regular octahedron are breaking, twisting at a certain angle ...
Truncated cubic prism, Truncated octahedral prism, Cuboctahedral prism, Rhombicuboctahedral prism, Truncated cuboctahedral prism, Snub cubic prism; Truncated dodecahedral prism, Truncated icosahedral prism, Icosidodecahedral prism, Rhombicosidodecahedral prism, Truncated icosidodecahedral prism, Snub dodecahedral prism; Uniform antiprismatic prism
The most obvious family of prismatic 4-polytopes is the polyhedral prisms, i.e. products of a polyhedron with a line segment. The cells of such a 4-polytopes are two identical uniform polyhedra lying in parallel hyperplanes (the base cells) and a layer of prisms joining them (the lateral cells).
Prismatic uniform polyhedron. Pentagrammic prism, Pentagrammic antiprism, Pentagrammic crossed-antiprism; Heptagrammic antiprism (7/2), Heptagrammic antiprism (7/3) Enneagrammic antiprism (9/2). Enneagrammic antiprism (9/4) Enneagrammic crossed-antiprism, Enneagrammic prism (9/2), Enneagrammic prism (9/4) Decagrammic prism, Decagrammic antiprism
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, ... Triangular prism: 3.4.4:
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 ...