Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:205AA GHM

Order: 20

Horizontal side: 205 Vertical side: 205

Elements: 4, 6, 6√2, 19√2, 34, 38, 42, 46, 49, 38√2, 55, 46√2, 49√2, 52√2, 76, 55√2, 95, 101, 104, 110.

Code: 1105 0 95 1041 104 205 522 156 153 1011 205 205 466 110 107 492 205 104 66 104 101 465 110 61 493 205 55 955 0 0 761 76 95 382 114 57 341 110 95 41 114 61 427 114 61 63 156 55 383 114 19 550 150 55 551 205 55 194 95 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)