tes mirror tile documented

tessellations/sample/123458_0_8314_a3a12_complex.tes

@@ -0,0 +1,13 @@
+## 123458_0_8314 A3+A12 example (5 vertices, 9 edges)
+h2.
+distunit(edge(12,4)/2)
+let(a3=regangle(1,3))
+let(a12=regangle(1,12))
+unittile(a3,a3,a3)
+unittile(a3,a3,a3)
+unittile(a12,a12,a12,a12,a12,a12,a12,a12,a12,a12,a12,a12)
+unittile(a3,a3,a3)
+unittile(a3,a3,a3)
+unittile(a12,a12,a12,*4)
+unittile(a3,a3,a3)
+conway("(0)(1 11'')(2 1'')(0')(1' 6'')(2' 8'')(0'')(2'' 0''')(3'' 0@6)(4'' 2@6)(5'' 0@4)(7'')(9'' 2@4)(10'' 1''')(2''' 1@5)(1@4 2@5)(0@5 1@6)")

tessellations/sample/123458_0_8314_a3a12_complex_2.tes

@@ -0,0 +1,11 @@
+## 123458_0_8314 A3+A12 example (5 vertices, 9 edges), simplified using mirrors
+h2.
+distunit(edge(12,4)/2)
+let(a3=regangle(1,3))
+let(a12=regangle(1,12))
+unittile(a3,a3,a3)
+unittile(a12,a12,a12,a12,a12,a12,a12,a12,a12,a12,a12,a12,|7)
+unittile(a3,a3,a3)
+unittile(a12,a12,a12,*4,|0)
+unittile(a3,a3,a3,|2)
+conway("(0)(1 11')(2 1')(0')(2' 0'')(3' 0@4)[9' 1''](2'' 1''')(0''' 1@4)")

tessellations/sample/12356_0_6329_a3a8c4_complex.tes

@@ -0,0 +1,21 @@
+## 12356_0_6329 A3+A8+C4 complex example (8 vertices, 16 edges)
+h2.
+distunit(arcmedge(3,3,8,8))
+let(a3=regangle(1,3))
+let(a8=regangle(1,8))
+let(c4=regangle(3,4))
+unittile(a3,*3)
+unittile(a3,*3)
+unittile(a8,a8,a8,a8,a8,a8,a8,a8)
+unittile(a3,a3,a3)
+unittile(a3,a3,a3)
+unittile(a8,a8,a8,a8,a8,a8,a8,a8)
+unittile(a3,a3,a3)
+unittile(a3,a3,a3)
+unittile(pi,c4,pi,pi,c4,pi,*2)
+unittile(a3,a3,a3)
+unittile(a3,a3,a3)
+unittile(a8,a8,a8,a8,a8,a8,a8,a8)
+unittile(a3,*3)
+unittile(a3,*3)
+conway("(0 1'')(0' 3'')(0'' 1''')(2'' 0''')(4'' 2''')(5'' 0@4)(6'' 0@6)(7'' 1@4)(2@4 1@5)(0@5 1@6)(2@5 2@6)(3@5 0@7)(4@5 5@8)(5@5 0@11)(6@5 1@8)(7@5 1@7)(2@7 0@8)(2@8 2@10)(3@8 4@11)(4@8 1@9)(0@9 1@11)(2@9 3@11)(1@10 5@11)(0@10 7@11)(2@11 0@12)(6@11 0@13)")

tessellations/sample/12356_0_6329_a3a8c4_complex_2.tes

@@ -0,0 +1,18 @@
+## 12356_0_6329 A3+A8+C4 complex example (8 vertices, 16 edges), simplified using mirrors
+h2.
+distunit(arcmedge(3,3,8,8))
+let(a3=regangle(1,3))
+let(a8=regangle(1,8))
+let(c4=regangle(3,4))
+unittile(a3,*3)
+unittile(a8,a8,a8,a8,a8,a8,a8,a8,|4)
+unittile(a3,a3,a3,|0)
+unittile(a3,a3,a3,|1)
+unittile(a8,a8,a8,a8,a8,a8,a8,a8,|2)
+unittile(a3,a3,a3,|0)
+unittile(a3,a3,a3,|1)
+unittile(pi,c4,pi,pi,c4,pi,*2,|0)
+unittile(a3,a3,a3)
+unittile(a8,a8,a8,a8,a8,a8,a8,a8,|0)
+unittile(a3,*3)
+conway("(0 1')(0' 1'')(2' 0'')(5' 0''')(6' 0@5)(2''' 1@4)(0@4 1@5)(3@4 0@6)(4@4 5@7)(5@4 0@9)(2@6 0@7)[2@7 1@8](3@7 4@9)(0@8 1@9)(2@8 3@9)(2@9 0@10)")

tessellations/sample/README.md

@@ -35,13 +35,19 @@ A typical tes file consists of the following parts:
 
 Some tessellations include tiles with rotational symmetry. For example, in the standard HyperRogue tiling 
 (bitruncated {7,3}), the heptagonal tiles have 7-fold rotational symmetry, and the hexagonal tiles have 3-fold
-rotational symmetry. In this case, it is convenient to not give an index to every edge of every tile, but only
+rotational symmetry. (We mean symmetries not only of the tile itself, but of the whole tiling.)
+In this case, it is convenient to not give an index to every edge of every tile, but only
 to the part which repeats (i.e., heptagons have 7 edges of index 0, and hexagons have 3 edges of index 0 and
 3 edges of index 1).
 
 Such situation can be defined with e.g. `tile(e0, a0, e1, a1, *3)` (this defines a hexagon with edges e0,e1,e0,e1,e0,e1
 and angles a0,a1,a0,a1,a0,a1; edges are indexed with 0,1,0,1,0,1).
 
+For mirror symmetries, use e.g. `tile(e0, a0, e1, a1, e2, a2, |2)`, which means that the tile has mirror symmetry,
+and edge i is the mirror image of tile 2-i. (For simplicity, you still need to write all the edge lengths and angles
+in this case, even if mirror symmetry could theoretically be used to infer some of this information.)
+When both rotational and mirror symmetries exist, put `*` before `|`.
+
 You can also use `repeat(tile_index, qty)` to make every edge index of tile tile_index repeat qty times, for example,
 `tile(e0, a0, e1, a1, e2, a2) repeat(0, 3)` has the same effect as tile(e0, a0, e1, a1, *3).