Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:216AT1of2 GHM

Order: 20

Horizontal side: 216 Vertical side: 216

Elements: 3, 3√2, 6, 6√2, 9, 10, 10√2, 15, 20, 15√2, 27, 26√2, 52, 72, 52√2, 92, 72√2, 82√2, 144, 108√2.

Code: 1445 0 72 1084 108 108 826 134 134 266 108 108 275 134 107 157 134 107 150 149 107 64 155 101 63 161 101 32 164 104 33 164 101 522 216 52 91 164 101 107 134 92 106 134 82 207 144 92 923 164 0 725 0 0 724 72 0 523 216 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)