Squaring.net >> IRTS >> PPIRTSS >> Order 19

**
Primitive Perfect Isosceles Right Triangled Square
**

**Title:** _d 19:156CD GHM

**Order:** 19

**Horizontal side:** 156 **Vertical side:** 156

**Elements:** 4√2, 8, 9, 8√2, 12, 12√2, 24, 18√2, 32, 23√2, 37, 28√2, 32√2, 46, 55, 55√2, 78, 101, 78√2.

**Code:** 1015 0 55 784 78 78 783 156 78 234 101 55 320 124 78 321 156 78 557 0 55 550 55 55 371 92 55 97 92 55 82 100 38 81 100 46 42 104 42 284 128 18 463 156 0 126 92 30 245 104 18 125 92 18 184 110 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)

101

78√2

78

23√2

32√2

32

55

55√2

37

9

8√2

8

4√2

28√2

46

12√2

24

12

18√2