Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328BV GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 2, 2√2, 4, 3√2, 6, 6√2, 9√2, 16√2, 32, 25√2, 50, 57, 57√2, 107, 114, 107√2, 114√2, 164, 214, 164√2.
Code: 2145 0 114 1644 164 164 1643 328 164 501 214 164 325 214 132 574 271 107 573 328 107 92 223 123 164 230 116 250 246 132 30 223 123 60 220 120 61 226 120 45 226 116 25 226 114 24 228 114 1145 0 0 1144 114 0 1070 221 107 1071 328 107
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)