Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:152AX GHM

Order: 19

Horizontal side: 152 Vertical side: 152

Elements: 3√2, 6, 6√2, 12, 10√2, 20, 15√2, 27, 20√2, 21√2, 30, 33, 40, 46, 61, 76, 61√2, 91, 76√2.

Code: 915 0 61 764 76 76 763 152 76 154 91 61 30 106 76 461 152 76 123 103 61 62 109 67 61 109 73 335 109 40 273 109 40 617 0 61 610 61 61 214 82 40 401 122 40 202 142 20 201 142 40 102 152 30 303 152 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)