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In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. [1] In a polygon, an edge is a line segment on the boundary, [2] and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides ...
Four numbering schemes for the uniform polyhedra are in common use, distinguished by letters: [C] Coxeter et al., 1954, showed the convex forms as figures 15 through 32; three prismatic forms, figures 33–35; and the nonconvex forms, figures 36–92.
The triangle has 3 vertices, each of which pairs with another triangle's vertex, making up another 3 edges. These edges form 3 parallelograms as other faces. [2] If the prism's edges are perpendicular to the base, the lateral faces are rectangles, and the prism is called a right triangular prism. [3]
A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two ... faces; the triangles ... triangle with three convex edges ...
Cartesian coordinates for the vertices of a rhombicosidodecahedron with an edge length of 2 centered at the origin are all even permutations of: [3] (±1, ±1, ±φ 3), (±φ 2, ±φ, ±2φ), (±(2+φ), 0, ±φ 2), where φ = 1 + √ 5 / 2 is the golden ratio. Therefore, the circumradius of this rhombicosidodecahedron is the common ...
The number of 1-faces (edges) of the n-simplex is the n-th triangle number, the number of 2-faces of the n-simplex is the (n − 1) th tetrahedron number, the number of 3-faces of the n-simplex is the (n − 2) th 5-cell number, and so on.
The possible faces are 3 - equilateral triangle; 4 - square; 5 - regular pentagon; 6 - regular hexagon; 8 - regular octagon; 10 - regular decagon; 5/2 - pentagram; 8/3 - octagram; 10/3 - decagram; Some faces will appear with reverse orientation which is written here as -3 - a triangle with reverse orientation (often written as 3/2)
A 3-simplex, with barycentric subdivisions of 1-faces (edges) 2-faces (triangles) and 3-faces (body). In geometry , a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane , a tetrahedron for points in three-dimensional space , etc.).