Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:254AA GHM
Order: 20
Horizontal side: 254 Vertical side: 254
Elements: 4√2, 5√2, 8, 8√2, 12√2, 24, 20√2, 24√2, 58, 58√2, 83, 88, 93, 98, 73√2, 108, 78√2, 83√2, 88√2, 98√2.
Code: 985 0 156 984 98 156 580 196 254 581 254 254 46 134 192 87 138 196 86 138 188 202 166 176 1081 254 196 120 134 192 240 122 180 241 146 180 933 166 83 882 254 88 782 78 78 734 73 83 883 254 0 54 78 78 830 83 83 831 166 83
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)