Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:178AI GHM

Order: 20

Horizontal side: 178 Vertical side: 178

Elements: 2, 2√2, 4, 4√2, 13√2, 26, 34, 26√2, 30√2, 48, 34√2, 39√2, 62, 48√2, 68, 72, 78, 80, 96, 72√2.

Code: 725 0 106 724 72 106 683 144 110 342 178 144 341 178 178 963 178 48 40 76 110 41 80 110 22 82 108 21 82 110 627 82 110 306 52 78 807 0 106 396 13 39 785 52 0 484 130 0 483 178 0 130 13 39 267 0 26 260 26 26

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)