Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:312AZ2of2 GHM
Order: 20
Horizontal side: 312 Vertical side: 312
Elements: 4, 4√2, 8, 6√2, 9, 12, 12√2, 18, 14√2, 23√2, 37, 46, 55√2, 110, 78√2, 101√2, 110√2, 156, 202, 156√2.
Code: 2025 0 110 1564 156 156 1563 312 156 461 202 156 142 216 142 554 257 101 786 234 78 83 216 134 42 220 138 43 220 134 375 220 101 66 202 128 127 208 134 126 208 122 185 202 110 1105 0 0 1104 110 0 93 220 101 1010 211 101 234 234 78
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)