Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:76AO1of2 GHM
Order: 20
Horizontal side: 76 Vertical side: 76
Elements: 2√2, 4, 5, 6, 5√2, 6√2, 12, 13, 16, 12√2, 17, 18, 21, 17√2, 19√2, 21√2, 34, 38, 42, 38√2.
Code: 425 0 34 384 38 38 383 76 38 41 42 38 175 42 21 174 59 21 196 57 19 345 0 0 124 12 22 123 24 22 187 24 34 133 42 21 64 18 16 63 24 16 50 29 21 51 34 21 217 34 21 210 55 21 24 57 19 161 34 16
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)