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There are three regular star polygons, {16/3}, {16/5}, {16/7}, using the same vertices, but connecting every third, fifth or seventh points. There are also three compounds: {16/2} is reduced to 2{8} as two octagons , {16/4} is reduced to 4{4} as four squares and {16/6} reduces to 2{8/3} as two octagrams , and finally {16/8} is reduced to 8{2 ...
16: 24: 10: 8{4} +2{8} Enneagonal prism: ... 10: 15: 7: 2: Yes: 2: 5{4}+2 ... The white polygon lines represent the "vertex figure" polygon. The colored faces are ...
Clusters of planigons which cannot tile the plane. Note the 8-cluster of V3.8.24 and the 10-cluster of V3.10.15 imply overlaps for the 24-gons and 15-gons, respectively. Also, V4.5.20 and V5 2.10 can generate lines and curves, but those cannot be completed without overlap.
Example dissections for select even-sided regular polygons 2m 6 8 10 12 14 16 18 20 24 30 40 50 Image Rhombs 3 6 10 15 21 ... 15.33450194 3.037186175: 0.9667663859 3. ...
1-uniform tilings include 3 regular tilings, and 8 semiregular ones, with 2 or more types of regular polygon faces. There are 20 2-uniform tilings, 61 3-uniform tilings, 151 4-uniform tilings, 332 5-uniform tilings and 673 6-uniform tilings. Each can be grouped by the number m of distinct vertex figures, which are also called m-Archimedean tilings.
A regular digon has both angles equal and both sides equal and is represented by Schläfli symbol {2}. It may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune. The digon is the simplest abstract polytope of rank 2. A truncated digon, t{2} is a square, {4}. An alternated digon, h{2} is a ...
There are 7 subgroup dihedral symmetries: (Dih 12, Dih 6, Dih 3), and (Dih 8, Dih 4, Dih 2 Dih 1), and 8 cyclic group symmetries: (Z 24, Z 12, Z 6, Z 3), and (Z 8, Z 4, Z 2, Z 1). These 16 symmetries can be seen in 22 distinct symmetries on the icositetragon. John Conway labels these by a letter and group order. [2]
1 32 • 2 31 • 3 21: Uniform 8-polytope: 8-simplex: 8-orthoplex • 8-cube: 8-demicube: 1 42 • 2 41 • 4 21: Uniform 9-polytope: 9-simplex: 9-orthoplex • 9-cube: 9-demicube: Uniform 10-polytope: 10-simplex: 10-orthoplex • 10-cube: 10-demicube: Uniform n-polytope: n-simplex: n-orthoplex • n-cube: n-demicube: 1 k2 • 2 k1 • k 21: n ...
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