Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:216AF1of2 GHM
Order: 20
Horizontal side: 216 Vertical side: 216
Elements: 4√2, 8, 8√2, 12√2, 13√2, 16√2, 26, 28, 26√2, 27√2, 28√2, 40, 54, 40√2, 54√2, 80, 108, 81√2, 95√2, 108√2.
Code: 1082 108 108 954 95 121 260 190 216 261 216 216 160 164 190 124 176 178 86 180 182 282 216 162 281 216 190 46 176 178 85 180 174 400 148 174 401 188 174 1083 216 54 136 95 121 807 108 134 276 81 81 810 81 81 544 162 0 543 216 0
The properties below may precede order:side in a tiling's title:
- c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
- d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
- e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
- i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
- r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.
Credit for Discovery
Just three people are credited with the discovery of Primitive Perfects:
Geoffrey H. Morley (GHM, England)
Jasper D. Skinner, II (JDS, United States)
William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)