Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328AD GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 1√2, 2, 2√2, 4, 10, 11√2, 22, 22√2, 44, 38√2, 44√2, 80, 84, 80√2, 84√2, 160, 164, 168, 122√2, 164√2.
Code: 1685 0 160 1644 164 164 1643 328 164 41 168 164 22 170 162 804 248 84 803 328 84 23 170 160 12 171 161 110 171 161 1607 0 160 386 122 122 107 160 160 227 160 150 220 182 150 447 160 128 440 204 128 1220 122 122 844 244 0 843 328 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)