Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:234CE GHM
Order: 20
Horizontal side: 234 Vertical side: 234
Elements: 1, 1√2, 6, 5√2, 8, 6√2, 9, 8√2, 11√2, 22, 28√2, 56, 61, 78, 56√2, 100, 78√2, 117, 156, 117√2.
Code: 1565 0 78 1174 117 117 1173 234 117 284 145 89 93 173 108 52 178 112 611 234 117 66 172 106 562 234 56 80 164 108 81 172 108 12 173 107 11 173 108 65 172 100 116 145 89 227 156 100 1003 178 0 785 0 0 784 78 0 563 234 0
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)