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A space that admits such a homeomorphism is called a triangulable space. Triangulations can also be used to define a piecewise linear structure for a space, if one exists. Triangulation has various applications both in and outside of mathematics, for instance in algebraic topology, in complex analysis, and in modeling.
However, the blue triangle has a ratio of 5:2 (=2.5), while the red triangle has the ratio 8:3 (≈2.667), so the apparent combined hypotenuse in each figure is actually bent. With the bent hypotenuse, the first figure actually occupies a combined 32 units, while the second figure occupies 33, including the "missing" square.
In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon).Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as a three-dimensional projection of a hypercube.
The stabilizer subgroup of the standard flag is the group of invertible upper triangular matrices.. More generally, the stabilizer of a flag (the linear operators on V such that () < for all i) is, in matrix terms, the algebra of block upper triangular matrices (with respect to an adapted basis), where the block sizes .
The four simplexes that can be fully represented in 3D space. In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is ...
The dihedral angle of a triangular cupola between square-to-triangle is approximately 125°, that between square-to-hexagon is 54.7°, and that between triangle-to-hexagon is 70.5°. Therefore, the dihedral angle of a cuboctahedron between square-to-triangle, on the edge where the base of two triangular cupolas are attached is 54.7° + 70.5 ...
The triangular space (also known as the medial triangular space, [1] upper triangular space, [2] medial axillary space or foramen omotricipitale [3]) is one of the three spaces found at the axillary space. The other two spaces are the quadrangular space and the triangular interval. [4]
In the following diagram, u and v are the given morphisms, and the primed letters are the cones of various maps (chosen so that every exact triangle has an X, a Y, and a Z letter). Various arrows have been marked with [1] to indicate that they are of "degree 1"; e.g. the map from Z ′ to X is in fact from Z ′ to X [1].