Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:364AF GHM
Order: 20
Horizontal side: 364 Vertical side: 364
Elements: 4√2, 8, 8√2, 12√2, 34, 34√2, 68, 68√2, 69√2, 73√2, 74√2, 108, 114, 142, 102√2, 148, 108√2, 114√2, 188, 148√2.
Code: 1485 0 216 1484 148 216 346 262 330 687 296 364 686 296 296 1883 262 142 1022 364 228 1146 250 114 1082 108 108 744 74 142 341 108 142 1425 108 0 734 181 69 46 250 138 87 254 142 86 254 134 696 181 69 122 262 126 1145 250 0 1083 108 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)