Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:188AB GHM

Order: 20

Horizontal side: 188 Vertical side: 188

Elements: 3√2, 5√2, 10, 10√2, 20, 25√2, 30√2, 44, 32√2, 33√2, 36√2, 56, 44√2, 64, 70, 72, 56√2, 88, 72√2, 112.

Code: 725 0 116 724 72 116 440 144 188 441 188 188 643 100 80 322 132 112 881 188 144 332 33 83 364 36 80 1123 132 0 562 188 56 30 33 83 306 0 50 707 30 80 563 188 0 252 25 25 50 25 25 203 20 0 102 30 10 101 30 20

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)