Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:216AD GHM
Order: 20
Horizontal side: 216 Vertical side: 216
Elements: 3√2, 6, 6√2, 9√2, 18, 30, 32, 40, 30√2, 32√2, 40√2, 60, 64, 48√2, 80, 60√2, 64√2, 96, 88√2, 108√2.
Code: 1082 108 108 884 88 128 400 176 216 401 216 216 480 136 176 801 216 176 321 120 128 642 184 64 641 184 128 322 216 96 183 108 90 92 117 99 30 117 99 60 114 96 61 120 96 963 216 0 300 90 90 301 120 90 600 60 60 601 120 60
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)