Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:100BC1of2 GHM

Order: 20

Horizontal side: 100 Vertical side: 100

Elements: 4, 4√2, 8, 8√2, 12, 14, 10√2, 14√2, 20, 15√2, 26, 28, 20√2, 30, 25√2, 28√2, 40, 30√2, 60, 50√2.

Code: 605 0 40 504 50 50 403 100 60 106 50 50 205 60 40 204 80 40 306 70 30 267 0 40 40 26 40 41 30 40 125 30 28 254 55 15 80 22 36 81 30 36 156 55 15 305 70 0 146 0 14 287 14 28 280 42 28 145 0 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)