Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:276AH GHM

Order: 19

Horizontal side: 276 Vertical side: 276

Elements: 8, 8√2, 9√2, 16, 15√2, 16√2, 19√2, 32, 25√2, 38, 50, 44√2, 88, 100, 88√2, 94√2, 100√2, 176, 138√2.

Code: 1765 0 100 1384 138 138 946 182 182 256 157 157 505 182 132 190 157 157 381 176 138 152 191 123 94 191 123 166 184 116 327 200 132 440 232 132 86 176 108 165 184 100 85 176 100 1005 0 0 1004 100 0 880 188 88 881 276 88

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)

176
138√2
94√2
25√2
50
19√2
38
15√2
9√2
16√2
32
44√2
8√2
16
8
100
100√2
88√2
88