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A 9-cube is a nine-dimensional hypercube with 512 vertices and 18 8-cubes as faces. Learn about its properties, projections, derived polytopes, and references from this Wikipedia article.
In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets . A uniform 9-polytope is one which is vertex-transitive , and constructed from uniform 8-polytope facets .
Britney Gallivan is a mathematician and origami artist who proved the minimum length of paper necessary to fold it in half a certain number of times. She also folded a 4,000-foot-long piece of toilet paper twelve times in 2002.
A tesseract or 4-cube is a four-dimensional analogue of a cube and a square, with eight cubical cells, 24 square faces, and 32 edges. Learn about its geometry, coordinates, nets, construction, and properties from this comprehensive Wikipedia article.
Modular origami is a technique of folding multiple sheets of paper into units and assembling them into flat or three-dimensional shapes. Learn about the origins, restrictions, modeling systems and notable artists of modular origami, and see diagrams and photos of various designs.
[9] [10] [11] There exist non-convex polyhedra that do not have nets, and it is possible to subdivide the faces of every convex polyhedron (for instance along a cut locus) so that the set of subdivided faces has a net. [5] In 2014 Mohammad Ghomi showed that every convex polyhedron admits a net after an affine transformation. [12]
A rhombic dodecahedron is a convex polyhedron with 12 rhombic faces, 24 edges, and 14 vertices of two types. It is a Catalan solid, the dual of the cuboctahedron, and has many properties and applications in geometry, crystallography, and biology.
There are 9 rectifications of the 9-cube. The zeroth is the 9-cube itself, and the 8th is the dual 9-orthoplex. Vertices of the rectified 9-cube are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-cube are located in the square face centers of the 9-cube. Vertices of the trirectified 9-orthoplex are located in the ...
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