Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:216AQ1of2 GHM
Order: 20
Horizontal side: 216 Vertical side: 216
Elements: 2, 2√2, 4, 3√2, 4√2, 5√2, 8, 7√2, 10, 22, 16√2, 27√2, 54, 76, 54√2, 70√2, 76√2, 108, 140, 108√2.
Code: 1405 0 76 1084 108 108 1083 216 108 274 135 81 223 162 86 547 162 108 546 162 54 56 135 81 105 140 76 74 147 79 46 150 82 87 154 86 166 146 70 36 147 79 45 150 78 25 150 76 24 152 76 765 0 0 764 76 0 700 146 70
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)