Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:166AX GHM

Order: 20

Horizontal side: 166 Vertical side: 166

Elements: 2√2, 4, 3√2, 4√2, 6, 18√2, 27, 21√2, 33, 36, 27√2, 54, 58, 60, 66, 48√2, 52√2, 54√2, 56√2, 112.

Code: 1127 0 166 603 112 106 275 112 139 274 139 139 216 145 145 63 145 139 32 148 142 363 148 106 182 166 124 337 112 139 663 166 58 520 52 106 484 100 58 44 104 54 43 108 54 22 110 56 581 166 58 560 110 56 545 0 0 544 54 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)