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On the other hand, 3 21 ∈ k 21 is the only semiregular polytope in the seventh dimension, also featuring a total of 702 6-faces of which 576 are 6-simplexes and 126 are 6-orthoplexes that contain 60 edges and 12 vertices, or collectively 72 one-dimensional and two-dimensional elements; with 126 the number of root vectors in , which are ...
These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners. The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine ...
There are many relations among the uniform polyhedra. [1] [2] [3] ... Number of vertices V, edges E, Faces F and number of faces by type. ... V 48,E 72,F 26=12{4}+8{6 ...
In the mathematical field of graph theory, a rhombicosidodecahedral graph is the graph of vertices and edges of the rhombicosidodecahedron, one of the Archimedean solids. It has 60 vertices and 120 edges, and is a quartic graph Archimedean graph. [5] Square centered Schlegel diagram
It follows that all vertices are congruent, ... There are infinitely many prisms and antiprisms, one for each regular polygon; the ones up to the 12-gonal cases are ...
The points, lines, and polygons of a polyhedron are referred to as its vertices, edges, and faces, respectively. [1] ... 72 Gyrate rhombicosidodecahedron: 60
The sum of the perpendiculars from a regular n-gon's vertices to any line tangent to the circumcircle equals n times the circumradius. [4]: p. 73 The sum of the squared distances from the vertices of a regular n-gon to any point on its circumcircle equals 2nR 2 where R is the circumradius. [4]: p. 73
In other words: the 30 vertices of the 600-cell which lie at arc distances of 90 degrees on its circumscribed hypersphere from a pair of opposite vertices, are the vertices of an icosidodecahedron. The wireframe figure of the 600-cell consists of 72 flat regular decagons.