Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:396AC GHM
Order: 20
Horizontal side: 396 Vertical side: 396
Elements: 16√2, 34, 30√2, 52, 60, 43√2, 52√2, 86, 92, 77√2, 120, 92√2, 136, 106√2, 152, 154, 122√2, 184, 138√2, 152√2.
Code: 1525 0 244 1524 152 244 920 304 396 921 396 396 603 212 244 302 242 274 1841 396 304 1363 242 138 1545 242 120 1222 122 122 1064 106 138 164 122 122 1380 138 138 524 190 86 523 242 86 345 242 86 774 319 43 1203 396 0 861 276 86 432 319 43
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)