Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:192AA GHM

Order: 20

Horizontal side: 192 Vertical side: 192

Elements: 4, 4√2, 13√2, 22, 16√2, 26, 32, 36, 28√2, 44, 48, 52, 44√2, 70, 52√2, 61√2, 92, 70√2, 100, 74√2.

Code: 742 74 118 614 61 131 483 122 144 707 122 192 706 122 122 136 61 131 267 74 144 1003 100 44 925 100 52 221 122 144 42 104 48 41 104 52 367 104 52 520 140 52 521 192 52 323 104 16 447 0 44 440 44 44 284 72 16 164 88 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)