Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:190AQ GHM

Order: 20

Horizontal side: 190 Vertical side: 190

Elements: 4√2, 8, 7√2, 8√2, 14, 12√2, 14√2, 16√2, 28, 28√2, 40, 42, 66, 68, 54√2, 82, 61√2, 68√2, 108, 122.

Code: 1225 0 68 1081 108 190 665 108 124 821 190 190 427 108 124 286 122 96 82 158 116 124 162 112 160 174 124 83 158 108 42 162 112 407 150 108 546 136 54 146 108 82 285 122 68 685 0 0 684 68 0 76 129 61 147 136 68 610 129 61

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)