Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:128AL1of8 GHM

Order: 20

Horizontal side: 128 Vertical side: 128

Elements: 4, 6, 6√2, 12, 12√2, 18, 13√2, 17√2, 18√2, 26, 21√2, 30, 34, 42, 30√2, 34√2, 60, 47√2, 68, 64√2.

Code: 685 0 60 644 64 64 476 81 81 170 81 81 41 68 64 307 68 64 300 98 64 605 0 0 124 12 48 123 24 48 187 24 60 180 42 60 261 68 60 64 18 42 63 24 42 421 60 42 212 81 21 134 81 21 340 94 34 341 128 34

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)