Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:450AH GHM
Order: 20
Horizontal side: 450 Vertical side: 450
Elements: 3√2, 12√2, 18, 15√2, 22, 24, 18√2, 30, 22√2, 44, 42√2, 53√2, 106, 106√2, 150, 194, 150√2, 172√2, 300, 225√2.
Code: 3005 0 150 2254 225 225 1726 278 278 536 225 225 422 320 236 126 308 224 245 320 212 303 308 194 152 323 209 34 323 209 180 326 212 181 344 212 1062 450 106 227 278 194 226 278 172 447 300 194 1943 344 0 1505 0 0 1504 150 0 1063 450 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)