Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:385AA GHM
Order: 20
Horizontal side: 385 Vertical side: 385
Elements: 22√2, 44, 44√2, 50√2, 75, 80, 88, 93, 100, 75√2, 120, 93√2, 137, 100√2, 142, 150, 155, 110√2, 160, 155√2.
Code: 1607 0 385 1100 160 385 881 248 385 442 292 341 1371 385 385 443 292 297 932 385 248 224 270 275 1423 292 155 506 0 225 1007 50 275 1006 50 175 1207 150 275 933 385 155 1505 0 75 807 150 155 1550 230 155 1551 385 155 755 0 0 754 75 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)