Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:238AE GHM

Order: 19

Horizontal side: 238 Vertical side: 238

Elements: 10, 18, 25, 18√2, 33, 36, 27√2, 28√2, 29√2, 33√2, 54, 56, 58, 63, 91, 119, 91√2, 147, 119√2.

Code: 1475 0 91 1194 119 119 1193 238 119 284 147 91 186 157 101 365 175 83 631 238 119 103 157 91 185 157 83 917 0 91 910 91 91 334 124 58 333 157 58 255 157 58 541 211 83 272 238 56 581 182 58 292 211 29 563 238 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)

147
119√2
119
28√2
18√2
36
63
10
18
91
91√2
33√2
33
25
54
27√2
58
29√2
56