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An icosagram is a 20-sided star polygon, represented by symbol {20/n}. There are three regular forms given by Schläfli symbols : {20/3} , {20/7} , and {20/9} . There are also five regular star figures (compounds) using the same vertex arrangement : 2{10} , 4{5} , 5{4} , 2{10/3} , 4{5/2} , and 10{2} .
The regular decagon has Dih 10 symmetry, order 20. There are 3 subgroup dihedral symmetries: Dih 5, Dih 2, and Dih 1, and 4 cyclic group symmetries: Z 10, Z 5, Z 2, and Z 1. These 8 symmetries can be seen in 10 distinct symmetries on the decagon, a larger number because the lines of reflections can either pass through vertices or edges.
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. ... Decagon – 10 sides; Hendecagon – 11 ... Icosagon – 20 sides ...
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 .
Pyritohedral symmetry has the symbol (3*2), [3 +,4], with order 24. Tetrahedral symmetry has the symbol (332), [3,3] +, with order 12. These lower symmetries allow geometric distortions from 20 equilateral triangular faces, instead having 8 equilateral triangles and 12 congruent isosceles triangles.
Full symmetry of the regular form is r12 and no symmetry is labeled a1. The regular hexagon has D 6 symmetry. There are 16 subgroups. There are 8 up to isomorphism: itself (D 6), 2 dihedral: (D 3, D 2), 4 cyclic: (Z 6, Z 3, Z 2, Z 1) and the trivial (e) These symmetries express nine distinct symmetries of a regular hexagon.
It has the same symmetry as the regular icosahedron, the icosahedral symmetry, and it also has the property of vertex-transitivity. [ 6 ] [ 7 ] The polygonal faces that meet for every vertex are one pentagon and two hexagons, and the vertex figure of a truncated icosahedron is 5 ⋅ 6 2 {\displaystyle 5\cdot 6^{2}} .
[20] The icosahedral graph has twelve vertices, the same number of vertices as a regular icosahedron. These vertices are connected by five edges from each vertex, making the icosahedral graph 5-regular. [21] The icosahedral graph is Hamiltonian, because it has a cycle that can visit each vertex exactly once. [22]