Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:364AH GHM
Order: 20
Horizontal side: 364 Vertical side: 364
Elements: 9, 9√2, 18, 18√2, 27√2, 30√2, 31√2, 60, 62, 61√2, 62√2, 120, 122, 93√2, 150, 120√2, 121√2, 122√2, 183, 151√2.
Code: 1512 151 213 1214 121 243 616 181 303 1227 242 364 1226 242 242 603 181 243 1835 181 120 304 151 213 1503 181 93 97 181 120 90 190 120 274 217 93 1200 244 120 1201 364 120 187 181 111 180 199 111 310 31 93 934 124 0 627 0 62 620 62 62
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)