Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:296AA GHM

Order: 20

Horizontal side: 296 Vertical side: 296

Elements: 10, 10√2, 17√2, 27√2, 32√2, 48, 59, 62, 64, 48√2, 62√2, 64√2, 93, 96, 110, 124, 93√2, 138, 110√2, 124√2.

Code: 1245 0 172 1244 124 172 480 248 296 481 296 296 1383 200 110 642 264 184 961 296 248 643 264 120 322 296 152 625 0 110 624 62 110 593 296 93 107 200 120 100 210 120 274 237 93 1105 0 0 1104 110 0 170 220 110 930 203 93 931 296 93

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)