Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:90AS GHM

Order: 20

Horizontal side: 90 Vertical side: 90

Elements: 1√2, 5, 5√2, 8, 8√2, 10√2, 11√2, 16, 12√2, 20, 15√2, 16√2, 25, 28, 20√2, 30, 32, 30√2, 60, 45√2.

Code: 605 0 30 454 45 45 206 70 70 253 70 45 205 70 50 55 70 45 104 80 40 116 79 39 154 60 30 50 75 45 80 70 40 81 78 40 122 90 28 14 79 39 323 62 0 162 78 16 161 78 32 305 0 0 304 30 0 283 90 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)