Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:64AI GHM

Order: 19

Horizontal side: 64 Vertical side: 64

Elements: 2, 2√2, 4, 5√2, 10, 12, 14, 10√2, 16, 12√2, 20, 16√2, 24, 17√2, 18√2, 20√2, 22√2, 24√2, 36.

Code: 245 0 40 244 24 40 363 48 28 162 64 48 161 64 64 143 64 34 202 20 20 124 12 28 20 50 34 21 52 34 127 52 34 176 47 17 47 48 32 103 52 22 184 30 10 220 42 22 54 47 17 203 20 0 102 30 10

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)