Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:91AE4of4 GHM
Order: 20
Horizontal side: 91 Vertical side: 91
Elements: 2√2, 4, 4√2, 8, 6√2, 10, 12, 14, 10√2, 20, 15√2, 26, 20√2, 30, 31, 40, 30√2, 31√2, 50, 61.
Code: 617 0 91 200 61 91 201 81 91 102 91 81 101 91 91 503 91 31 263 41 45 407 41 71 150 15 45 121 27 45 85 27 37 141 41 45 45 27 33 44 31 33 60 35 37 24 29 31 314 60 0 313 91 0 307 0 30 300 30 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)