Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:206AC GHM
Order: 20
Horizontal side: 206 Vertical side: 206
Elements: 1, 3√2, 12√2, 18, 15√2, 24, 17√2, 18√2, 24√2, 34, 35, 34√2, 35√2, 36√2, 68, 68√2, 102, 104, 86√2, 103√2.
Code: 1047 0 206 680 104 206 681 172 206 342 206 172 341 206 206 866 120 86 360 36 138 244 60 114 243 84 114 187 84 138 186 84 120 355 102 103 354 137 103 32 87 117 150 87 117 124 72 102 17 102 103 1030 103 103 174 120 86 1027 0 102
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)