Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:366AB GHM

Order: 20

Horizontal side: 366 Vertical side: 366

Elements: 3√2, 26, 26√2, 52, 56, 78, 56√2, 106, 78√2, 112, 80√2, 115, 121, 124, 130, 136, 115√2, 121√2, 124√2, 130√2.

Code: 1305 0 236 1304 130 236 523 260 314 262 286 340 1061 366 366 263 286 314 802 366 260 780 208 314 781 286 314 1363 366 124 1155 0 121 1154 115 121 1123 230 124 562 286 180 561 286 236 30 118 124 1244 242 0 1243 366 0 1217 0 121 1210 121 121

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)