Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:366AI GHM
Order: 20
Horizontal side: 366 Vertical side: 366
Elements: 10, 8√2, 10√2, 16, 20, 20√2, 27√2, 70, 94, 70√2, 102, 78√2, 124, 140, 102√2, 105√2, 156, 132√2, 194, 148√2.
Code: 1565 0 210 1484 148 218 1403 296 226 702 366 296 701 366 366 1943 366 102 86 148 218 167 156 226 943 172 132 1247 172 226 1052 105 105 784 78 132 274 105 105 1320 132 132 204 152 112 203 172 112 104 162 102 103 172 102 1024 264 0 1023 366 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)