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A convex polytope, like any compact convex subset of R n, is homeomorphic to a closed ball. Let m denote the dimension of the polytope. If the polytope is full-dimensional, then m = n. The convex polytope therefore is an m-dimensional manifold with boundary, its Euler characteristic is 1, and its fundamental group is trivial.
For the regular octadecagon, m=9, and it can be divided into 36: 4 sets of 9 rhombs. This decomposition is based on a Petrie polygon projection of a 9-cube , with 36 of 4608 faces. The list OEIS : A006245 enumerates the number of solutions as 112018190, including up to 18-fold rotations and chiral forms in reflection.
A function (in black) is convex if and only if the region above its graph (in green) is a convex set. A graph of the bivariate convex function x 2 + xy + y 2. Convex vs. Not convex. In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph ...
convex, Hanner polytope. In geometry, a 9-orthoplex or 9- cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cells 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces . It has two constructed forms, the first being regular ...
Properties. A wedge is a polyhedron of a rectangular base, with the faces are two isosceles triangles and two trapezoids that meet at the top of an edge. [1]. A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles, trapezoids, and parallelograms; [2] the wedge is an example of ...
In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-cube.. There are 32 hexications for the 7-cube, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. 20 are represented here, while 12 are more easily constructed from the 7-orthoplex.
In eight-dimensional geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube. Alternate names [ edit ] Truncated demiocteract
Stericated 5-cubes. In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations ( sterication) of the regular 5-cube . There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and truncation. The simple stericated 5-cube is also called an ...