Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:127AC GHM
Order: 20
Horizontal side: 127 Vertical side: 127
Elements: 10, 8√2, 12, 16, 12√2, 21, 22, 24, 21√2, 32, 24√2, 37, 42, 32√2, 48, 37√2, 58, 42√2, 45√2, 53√2.
Code: 532 53 74 454 45 82 370 90 127 371 127 127 86 45 82 167 53 90 483 69 42 242 93 66 581 127 90 243 93 42 122 105 54 123 105 42 225 105 32 216 0 21 425 21 0 424 63 0 103 105 32 320 95 32 321 127 32 215 0 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)