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Regular convex and star polygons with 3 to 12 vertices, labeled with their Schläfli symbols A regular star polygon is a self-intersecting, equilateral, and equiangular polygon . A regular star polygon is denoted by its Schläfli symbol { p / q }, where p (the number of vertices) and q (the density ) are relatively prime (they share no factors ...
The stellation process can be applied to higher dimensional polytopes as well. A stellation diagram of an n-polytope exists in an (n − 1)-dimensional hyperplane of a given facet. For example, in 4-space, the great grand stellated 120-cell is the final stellation of the regular 4-polytope 120-cell.
A truncated square is an octagon, t{4}={8}. A quasitruncated square, inverted as {4/3}, is an octagram, t{4/3}={8/3}. [2] The uniform star polyhedron stellated truncated hexahedron, t'{4,3}=t{4/3,3} has octagram faces constructed from the cube in this way. It may be considered for this reason as a three-dimensional analogue of the octagram.
The obelisk in the center of the Plaza de Europa in Zaragoza, Spain, is surrounded by twelve stellated octahedral lampposts, shaped to form a three-dimensional version of the Flag of Europe. [ 6 ] Some modern mystics have associated this shape with the "merkaba", [ 7 ] which according to them is a "counter-rotating energy field" named from an ...
These include the 12 blended apeirohedra created by blends with the Euclidean planar apeirohedra, and 18 pure apeirohedra, which cannot be expressed as a non-trivial blend including the planar apeirohedra and the three 3-dimensional apeirohedra above. The 3-dimensional pure apeirohedra are: {4,6|4}, the mucube {∞,6} 4,4, the Petrial of the mucube
The Sierpiński tetrahedron or tetrix is the three-dimensional analogue of the Sierpiński triangle, formed by repeatedly shrinking a regular tetrahedron to one half its original height, putting together four copies of this tetrahedron with corners touching, and then repeating the process.
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general kinds of star polyhedron: Polyhedra which self-intersect in a repetitive way. Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way.
The convex regular dodecahedron also has three stellations, all of which are regular star dodecahedra.They form three of the four Kepler–Poinsot polyhedra.They are the small stellated dodecahedron {5/2, 5}, the great dodecahedron {5, 5/2}, and the great stellated dodecahedron {5/2, 3}.