Search results
Results from the WOW.Com Content Network
Download QR code; Print/export ... Fundamental convex regular and uniform polytopes in dimensions 2–10. Family: A n: B n: I 2 (p) ... 9-orthoplex • 9-cube: 9 ...
In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube. 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 ...
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 a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices , and 120 edges .
Download QR code; Print/export ... Convex Nonconvex Convex Euclidean tessellations ... 9-simplex: 9-cube: 9-orthoplex: 10-simplex: 10-cube:
For the cube the extended ƒ-vector is (1,8,12,6,1) and for the octahedron it is (1,6,12,8,1). Although the vectors for these example polyhedra are unimodal (the coefficients, taken in left to right order, increase to a maximum and then decrease), there are higher-dimensional polytopes for which this is not true.
The rhombic dodecahedron can be viewed as the convex hull of the union of the vertices of a cube and an octahedron where the edges intersect perpendicularly. The six vertices where four rhombi meet correspond to the vertices of the octahedron, while the eight vertices where three rhombi meet correspond to the vertices of the cube.
The icosahedron, snub cube and snub dodecahedron are the only three convex ones. They are obtained by snubification of the truncated octahedron, truncated cuboctahedron and the truncated icosidodecahedron - the three convex truncated quasiregular polyhedra. The only snub polyhedron with the chiral octahedral group of symmetries is the snub cube.
[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]