Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:102AC GHM

Order: 20

Horizontal side: 102 Vertical side: 102

Elements: 6√2, 7√2, 12, 9√2, 18, 20, 16√2, 18√2, 28, 20√2, 21√2, 32, 23√2, 36, 26√2, 28√2, 42, 30√2, 36√2, 42√2.

Code: 425 0 60 424 42 60 180 84 102 181 102 102 360 66 84 361 102 84 302 30 30 214 21 39 96 21 39 325 30 16 264 56 22 200 82 48 201 102 48 76 23 23 66 56 22 127 62 28 280 74 28 281 102 28 230 23 23 164 46 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)