Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:366AC GHM
Order: 20
Horizontal side: 366 Vertical side: 366
Elements: 9√2, 28, 30, 28√2, 30√2, 60, 74, 60√2, 92, 101, 74√2, 118, 119, 128, 101√2, 146, 164, 119√2, 128√2, 146√2.
Code: 1465 0 220 1464 146 220 1183 292 248 742 366 292 741 366 366 1643 366 128 280 174 248 281 202 248 602 262 188 601 262 248 302 292 218 301 292 248 1015 0 119 1014 101 119 923 202 128 90 110 128 1284 238 0 1283 366 0 1197 0 119 1190 119 119
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)