Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:312AA2of2 GHM
Order: 20
Horizontal side: 312 Vertical side: 312
Elements: 8√2, 16, 16√2, 24, 28, 24√2, 28√2, 48, 39√2, 50√2, 53√2, 78, 56√2, 106, 78√2, 128, 103√2, 156, 117√2, 156√2.
Code: 1565 0 156 1564 156 156 1036 209 209 530 209 209 782 78 78 1174 117 39 280 234 156 281 262 156 502 312 106 1283 206 0 165 206 112 164 222 112 240 238 128 241 262 128 562 262 56 84 214 104 1063 312 0 481 262 104 783 78 0 392 117 39
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)