Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:292AB4of4 GHM
Order: 20
Horizontal side: 292 Vertical side: 292
Elements: 4√2, 8, 8√2, 14, 16, 12√2, 24, 19√2, 28, 26√2, 66, 47√2, 80, 66√2, 80√2, 132, 146, 106√2, 160, 146√2.
Code: 1605 0 132 1464 146 146 1463 292 146 141 160 146 192 179 127 664 226 80 663 292 80 1327 0 132 266 106 106 287 132 132 243 160 108 470 179 127 46 132 104 87 136 108 86 136 100 167 144 108 1060 106 106 122 144 92 804 212 0 803 292 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)