Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:160BF GHM
Order: 20
Horizontal side: 160 Vertical side: 160
Elements: 1√2, 2, 2√2, 3√2, 6, 10, 10√2, 16√2, 20√2, 32, 24√2, 40, 32√2, 40√2, 60, 44√2, 48√2, 80, 96, 80√2.
Code: 965 0 64 804 80 80 803 160 80 104 90 70 103 100 70 607 100 80 406 120 40 61 96 70 32 99 67 24 98 68 23 100 68 14 99 67 246 76 44 322 32 32 484 48 16 440 76 44 206 100 20 405 120 0 323 32 0 162 48 16
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)