Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:102AF GHM

Order: 20

Horizontal side: 102 Vertical side: 102

Elements: 2√2, 4, 4√2, 5√2, 8, 8√2, 16, 20, 21, 16√2, 20√2, 30, 31, 40, 42, 30√2, 31√2, 36√2, 40√2, 41√2.

Code: 427 0 102 400 42 102 401 82 102 202 102 82 201 102 102 416 61 41 26 0 60 47 2 62 46 2 58 87 6 62 86 6 54 167 14 62 166 14 46 312 61 31 311 61 62 217 61 62 302 30 30 52 66 36 360 66 36 303 30 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)