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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.
The regular icosagon has Schläfli symbol {20}, and can also be constructed as a truncated decagon, t{10}, or a twice-truncated pentagon, tt{5}. One interior angle in a regular icosagon is 162°, meaning that one exterior angle would be 18°.
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.
The resulting polyhedron has 20 equilateral triangles as its faces, 30 edges, and 12 vertices. It is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedra are constructed from the regular icosahedron.
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. ... Decagon – 10 sides; Hendecagon – 11 ... Icosagon – 20 sides ...
It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational ... and 20 sides respectively. ... 10: 20{3}+12 5 ...
A rhombic icosahedron. The rhombic icosahedron is a polyhedron shaped like an oblate sphere.Its 20 faces are congruent golden rhombi; [1] 3, 4, or 5 faces meet at each vertex. It has 5 faces (green on top figure) meeting at each of its 2 poles; these 2 vertices lie on its axis of 5-fold symmetry, which is perpendicular to 5 axes of 2-fold symmetry through the midpoints of opposite equatorial ...
The four sides can be split into two pairs of adjacent equal-length sides. [7] One diagonal crosses the midpoint of the other diagonal at a right angle, forming its perpendicular bisector. [9] (In the concave case, the line through one of the diagonals bisects the other.) One diagonal is a line of symmetry.