Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:454AA GHM
Order: 20
Horizontal side: 454 Vertical side: 454
Elements: 8, 8√2, 12, 11√2, 16, 12√2, 22, 16√2, 22√2, 33√2, 44√2, 61√2, 122, 154, 122√2, 178, 154√2, 166√2, 300, 227√2.
Code: 3005 0 154 2274 227 227 1666 288 288 616 227 227 442 332 244 336 299 211 1222 454 122 110 299 211 227 288 200 220 310 200 127 288 178 126 288 166 165 300 162 164 316 162 1783 332 0 85 300 154 84 308 154 1545 0 0 1544 154 0 1223 454 0
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)