Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:234BX GHM
Order: 20
Horizontal side: 234 Vertical side: 234
Elements: 1√2, 2, 2√2, 3√2, 4√2, 5√2, 10, 10√2, 15, 24, 27√2, 39, 54, 54√2, 78, 102, 78√2, 90√2, 156, 117√2.
Code: 1565 0 78 1174 117 117 906 144 144 270 144 144 391 156 117 157 156 117 50 171 117 100 166 112 101 176 112 42 180 108 36 177 105 542 234 54 10 177 105 27 176 104 20 178 104 247 156 102 1023 180 0 785 0 0 784 78 0 543 234 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)