Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:328AX GHM

Order: 20

Horizontal side: 328 Vertical side: 328

Elements: 8√2, 32, 24√2, 38, 44, 32√2, 48, 38√2, 40√2, 41√2, 64, 48√2, 82, 96, 82√2, 120, 126, 123√2, 208, 164√2.

Code: 2085 0 120 1644 164 164 1236 205 205 410 205 205 441 208 164 382 246 126 381 246 164 822 328 82 1263 246 0 1205 0 0 961 96 120 482 144 72 404 136 80 320 176 120 321 208 120 86 136 80 647 144 88 823 328 0 483 144 24 244 120 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)