Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:242AC GHM
Order: 20
Horizontal side: 242 Vertical side: 242
Elements: 10, 10√2, 11√2, 20, 20√2, 40, 44, 35√2, 62, 66, 70, 62√2, 88, 92, 66√2, 75√2, 77√2, 110, 114, 88√2.
Code: 1105 0 132 754 75 167 403 150 202 202 170 222 921 242 242 203 170 202 102 180 212 103 180 202 622 242 150 356 75 167 707 110 202 1143 180 88 623 242 88 662 66 66 661 66 132 447 66 132 112 77 77 884 154 0 883 242 0 770 77 77
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)