Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:226AG GHM
Order: 20
Horizontal side: 226 Vertical side: 226
Elements: 5√2, 10, 10√2, 13√2, 14√2, 15√2, 30, 30√2, 58, 45√2, 56√2, 80, 58√2, 84, 86, 90, 70√2, 110, 112, 84√2.
Code: 1107 0 226 903 110 136 452 155 181 584 168 168 583 226 168 130 155 181 1123 142 56 847 142 168 846 142 84 56 15 131 107 20 136 106 20 126 807 30 136 150 15 131 307 0 116 306 0 86 865 0 0 142 156 70 700 156 70 564 86 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)