Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:218AE GHM
Order: 20
Horizontal side: 218 Vertical side: 218
Elements: 1√2, 11√2, 12√2, 13√2, 24, 26, 20√2, 23√2, 26√2, 40, 46, 52, 40√2, 80, 86, 63√2, 92, 66√2, 132, 109√2.
Code: 1325 0 86 1094 109 109 636 155 155 463 155 109 245 155 131 112 166 120 124 167 119 130 179 131 803 166 40 12 167 119 267 166 118 260 192 118 234 132 86 527 166 92 923 218 0 865 0 0 664 66 20 206 66 20 405 86 0 404 126 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)