Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:216AS GHM

Order: 20

Horizontal side: 216 Vertical side: 216

Elements: 1√2, 2, 2√2, 3, 3√2, 6, 9, 25, 25√2, 50, 42√2, 66, 49√2, 50√2, 75, 66√2, 100, 75√2, 125, 141.

Code: 1417 0 216 500 141 216 501 191 216 252 216 191 251 216 216 1253 216 66 496 42 117 1007 91 166 420 42 117 757 0 75 750 75 75 91 84 75 65 84 69 35 84 66 34 87 66 10 90 69 20 89 68 21 91 68 664 150 0 663 216 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)