Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:256BC GHM
Order: 20
Horizontal side: 256 Vertical side: 256
Elements: 6, 5√2, 6√2, 15√2, 20√2, 30, 25√2, 40, 30√2, 50, 58, 64, 58√2, 61√2, 64√2, 70√2, 122, 128, 134, 128√2.
Code: 1347 0 256 616 73 195 1227 134 256 1286 128 128 150 73 195 586 0 122 302 88 150 301 88 180 405 88 140 56 83 145 250 83 145 204 108 120 706 58 70 62 134 134 1285 128 0 585 0 64 507 58 120 65 58 64 647 0 64 640 64 64
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)