Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:368AW GHM
Order: 20
Horizontal side: 368 Vertical side: 368
Elements: 5√2, 8, 10, 8√2, 10√2, 15√2, 30, 50, 50√2, 84, 92, 100, 84√2, 88√2, 92√2, 100√2, 176, 184, 192, 184√2.
Code: 1927 0 368 886 104 280 1767 192 368 1846 184 184 156 89 265 305 104 250 50 89 265 846 0 176 107 84 260 100 94 260 507 84 250 500 134 250 1007 84 200 1006 84 100 82 192 192 1845 184 0 845 0 92 85 84 92 927 0 92 920 92 92
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)