Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:158AA GHM

Order: 20

Horizontal side: 158 Vertical side: 158

Elements: 6√2, 12, 13, 10√2, 12√2, 20, 18√2, 30, 23√2, 33, 36, 42, 30√2, 46, 33√2, 46√2, 66, 56√2, 92, 79√2.

Code: 925 0 66 794 79 79 566 102 102 230 102 102 131 92 79 337 92 79 330 125 79 665 0 0 421 42 66 307 42 66 300 72 66 201 92 66 104 102 36 460 112 46 461 158 46 125 42 24 124 54 24 186 48 18 367 66 36 64 48 18

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)