Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:158BD GHM

Order: 19

Horizontal side: 158 Vertical side: 158

Elements: 4√2, 6, 8, 8√2, 11√2, 16, 22, 17√2, 20√2, 30, 34, 38, 45, 34√2, 62, 79, 62√2, 96, 79√2.

Code: 965 0 62 794 79 79 793 158 79 174 96 62 110 113 79 451 158 79 63 102 62 227 102 68 303 124 38 342 158 34 627 0 62 620 62 62 204 82 42 163 102 46 46 82 42 85 86 38 84 94 38 381 124 38 343 158 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)

96
79√2
79
17√2
11√2
45
6
22
30
34√2
62
62√2
20√2
16
4√2
8
8√2
38
34