Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:74AF GHM
Order: 20
Horizontal side: 74 Vertical side: 74
Elements: 1, 1√2, 2, 2√2, 4, 6, 5√2, 8, 6√2, 7√2, 11, 12, 12√2, 24, 26, 24√2, 25√2, 26√2, 48, 37√2.
Code: 485 0 26 374 37 37 256 49 49 123 49 37 62 55 43 70 55 43 111 48 37 17 48 37 52 53 31 61 54 36 87 54 36 120 62 36 10 53 31 43 52 26 22 54 28 21 54 30 265 0 0 264 26 0 240 50 24 241 74 24
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)