Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:72AU GHM
Order: 20
Horizontal side: 72 Vertical side: 72
Elements: 2√2, 4, 3√2, 4√2, 6, 8, 6√2, 9, 8√2, 12, 14, 14√2, 21, 28, 21√2, 30, 33, 39, 42, 30√2.
Code: 427 0 72 216 21 51 147 42 72 140 56 72 84 64 64 83 72 64 44 68 60 43 72 60 24 70 58 306 42 30 287 42 58 213 21 30 125 21 39 95 21 30 64 27 33 63 33 33 395 33 0 34 30 30 333 33 0 307 0 30
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)