Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:450AE GHM
Order: 20
Horizontal side: 450 Vertical side: 450
Elements: 12, 11√2, 12√2, 18, 24, 18√2, 20√2, 24√2, 40, 31√2, 48, 55√2, 110, 150, 110√2, 190, 150√2, 170√2, 300, 225√2.
Code: 3005 0 150 2254 225 225 1706 280 280 556 225 225 485 280 232 312 311 201 244 304 208 243 328 208 122 340 220 123 340 208 1102 450 110 184 322 190 183 340 190 110 311 201 206 280 170 407 300 190 1903 340 0 1505 0 0 1504 150 0 1103 450 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)