Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:136AX GHM

Order: 18

Horizontal side: 136 Vertical side: 136

Elements: 1√2, 2, 2√2, 3√2, 6, 6√2, 12, 11√2, 22, 23, 23√2, 45, 46, 45√2, 46√2, 68, 90, 68√2.

Code: 905 0 46 684 68 68 683 136 68 221 90 68 125 90 56 234 113 45 233 136 45 65 90 50 64 96 50 110 102 56 22 92 48 34 93 47 23 92 46 12 93 47 465 0 0 464 46 0 450 91 45 451 136 45

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)