Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:190AB GHM

Order: 20

Horizontal side: 190 Vertical side: 190

Elements: 8, 10, 10√2, 20, 20√2, 29√2, 30√2, 50, 37√2, 54, 40√2, 58, 62, 66, 74, 54√2, 58√2, 62√2, 66√2, 70√2.

Code: 747 0 190 540 74 190 541 128 190 627 128 190 626 128 128 200 20 136 201 40 136 102 50 126 404 80 96 700 120 136 81 128 136 103 50 116 302 80 96 582 58 58 501 50 116 374 87 29 660 124 66 661 190 66 583 58 0 292 87 29

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)