Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:254AB GHM
Order: 20
Horizontal side: 254 Vertical side: 254
Elements: 5√2, 8√2, 16, 16√2, 24√2, 50, 58, 66, 68, 50√2, 73, 58√2, 83, 88, 98, 73√2, 108, 83√2, 88√2, 98√2.
Code: 985 0 156 984 98 156 663 196 188 582 254 196 581 254 254 1083 254 88 86 122 180 167 130 188 166 130 172 502 196 138 501 196 188 240 122 180 735 0 83 734 73 83 683 146 88 50 78 88 884 166 0 883 254 0 837 0 83 830 83 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)