Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:312BK GHM
Order: 20
Horizontal side: 312 Vertical side: 312
Elements: 3√2, 4√2, 6, 6√2, 12, 16√2, 24, 20√2, 32, 24√2, 40, 44√2, 56√2, 106, 112, 100√2, 103√2, 106√2, 206, 156√2.
Code: 2065 0 106 1564 156 156 1123 312 200 446 156 156 405 200 160 564 256 144 1006 212 100 242 224 136 204 220 140 160 240 160 46 220 140 327 224 144 243 224 112 64 206 106 63 212 106 127 212 112 1065 0 0 1064 106 0 36 209 103 1030 209 103
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)