Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:312AW1of2 GHM
Order: 20
Horizontal side: 312 Vertical side: 312
Elements: 2√2, 4, 4√2, 8, 10√2, 12√2, 18, 14√2, 20, 23√2, 46, 55, 55√2, 101, 110, 101√2, 110√2, 156, 202, 156√2.
Code: 2025 0 110 1564 156 156 1563 312 156 461 202 156 122 214 144 554 257 101 553 312 101 106 204 134 205 214 124 20 204 134 47 202 132 46 202 128 85 206 124 185 202 110 144 220 110 230 234 124 1105 0 0 1104 110 0 1010 211 101 1011 312 101
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)