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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.
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
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 tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid , which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point.
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 .
3D model of a truncated icosahedron. In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. . Intuitively, it may be regarded as footballs (or soccer balls) that are typically patterned with white hexagons and black pentag
A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. The relative position and angle of the axes is typically uninformative, but various heuristics, such as algorithms that plot data as the maximal ...
There is no need for layering to create a part, because a single fabric provides the full three-dimensional reinforcement. The 3-D woven fabric is a variant of the 2D weaving process, and it is an extension of the very old technique of creating double and triple woven cloth. 3D weaving allows the production of fabrics up to 10 cm in thickness. [1]