Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:384AC GHM
Order: 20
Horizontal side: 384 Vertical side: 384
Elements: 4, 3√2, 4√2, 6, 8, 6√2, 8√2, 16, 20√2, 28√2, 40, 48√2, 96, 130, 96√2, 127√2, 130√2, 192, 254, 192√2.
Code: 2545 0 130 1924 192 192 1923 384 192 484 240 144 403 288 152 967 288 192 966 288 96 86 240 144 165 248 136 204 268 132 286 260 124 64 254 130 63 260 130 47 260 136 40 264 136 87 260 132 1305 0 0 1304 130 0 36 257 127 1270 257 127
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)