Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:188AA GHM

Order: 20

Horizontal side: 188 Vertical side: 188

Elements: 8, 13√2, 26, 26√2, 30√2, 44, 32√2, 46, 33√2, 38√2, 56, 60, 44√2, 66, 68, 76, 56√2, 60√2, 88, 66√2.

Code: 687 0 188 386 30 150 767 68 188 440 144 188 441 188 188 300 30 150 320 100 144 881 188 144 602 60 60 601 60 120 85 60 112 262 86 86 261 86 112 132 99 99 461 132 112 562 188 56 330 99 99 660 66 66 661 132 66 563 188 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)