Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:204AK GHM

Order: 20

Horizontal side: 204 Vertical side: 204

Elements: 6√2, 7√2, 12, 14, 12√2, 18, 18√2, 28, 20√2, 36, 40, 54, 41√2, 61, 68, 82, 61√2, 68√2, 136, 143.

Code: 1435 0 61 1361 136 204 682 204 136 681 204 204 543 204 82 143 150 68 187 150 82 186 150 64 367 168 82 823 204 0 74 143 61 283 150 40 122 162 52 617 0 61 610 61 61 414 102 20 123 162 40 62 168 46 206 102 20 407 122 40

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)