Expression 15: StartAbsoluteValue, "x" plus left parenthesis, 1 plus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , right parenthesis , EndAbsoluteValue equals left parenthesis, StartFraction, 1 plus StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction , right parenthesis plus StartFraction, StartAbsoluteValue, "y" plus left parenthesis, 1 plus StartNestedFraction, StartRoot, 3 , EndRoot NestedOver 2 , EndNestedFraction , right parenthesis , EndAbsoluteValue Over StartRoot, 3 , EndRoot , EndFraction left brace, negative 2 minus StartRoot, 3 , EndRoot less than or equal to "y" less than or equal to 0 , right bracex+1+32=1+323+y+1+323−2−3≤y≤0
15
Expression 16: "x" equals negative 1 minus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction left brace, negative StartFraction, 4 plus 3 StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction less than or equal to "y" less than or equal to negative StartFraction, 2 plus StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction , right bracex=−1−32−4+3323≤y≤−2+323
16
Expression 17: "y" equals negative 1 minus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction left brace, negative StartFraction, 4 plus 3 StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction less than or equal to "x" less than or equal to negative StartFraction, 2 plus StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction , right bracey=−1−32−4+3323≤x≤−2+323
17
Dual of Uniform Tiling
18
Expression 19: "x" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "X" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis equals 0 left brace, negative 2 minus StartRoot, 3 , EndRoot less than or equal to "y" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "Y" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis less than or equal to 0 , right bracex−2+3XA−3=0−2−3≤y−2+3YA−3≤0
19
Expression 20: "y" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "Y" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis equals 0 left brace, negative 2 minus StartRoot, 3 , EndRoot less than or equal to "x" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "X" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis less than or equal to 0 , right bracey−2+3YA−3=0−2−3≤x−2+3XA−3≤0
20
Expression 21: StartAbsoluteValue, "y" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "Y" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis plus left parenthesis, 1 plus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , right parenthesis , EndAbsoluteValue equals left parenthesis, StartFraction, 1 plus StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction , right parenthesis plus StartFraction, StartAbsoluteValue, "x" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "X" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis plus left parenthesis, 1 plus StartNestedFraction, StartRoot, 3 , EndRoot NestedOver 2 , EndNestedFraction , right parenthesis , EndAbsoluteValue Over StartRoot, 3 , EndRoot , EndFraction left brace, negative 2 minus StartRoot, 3 , EndRoot less than or equal to "x" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "X" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis less than or equal to 0 , right bracey−2+3YA−3+1+32=1+323+x−2+3XA−3+1+323−2−3≤x−2+3XA−3≤0
21
Expression 22: StartAbsoluteValue, "x" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "X" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis plus left parenthesis, 1 plus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , right parenthesis , EndAbsoluteValue equals left parenthesis, StartFraction, 1 plus StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction , right parenthesis plus StartFraction, StartAbsoluteValue, "y" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "Y" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis plus left parenthesis, 1 plus StartNestedFraction, StartRoot, 3 , EndRoot NestedOver 2 , EndNestedFraction , right parenthesis , EndAbsoluteValue Over StartRoot, 3 , EndRoot , EndFraction left brace, negative 2 minus StartRoot, 3 , EndRoot less than or equal to "y" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "Y" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis less than or equal to 0 , right bracex−2+3XA−3+1+32=1+323+y−2+3YA−3+1+323−2−3≤y−2+3YA−3≤0
22
Expression 23: "x" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "X" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis equals negative 1 minus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction left brace, negative StartFraction, 4 plus 3 StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction less than or equal to "y" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "Y" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis less than or equal to negative StartFraction, 2 plus StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction , right bracex−2+3XA−3=−1−32−4+3323≤y−2+3YA−3≤−2+323
23
Expression 24: "y" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "Y" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis equals negative 1 minus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction left brace, negative StartFraction, 4 plus 3 StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction less than or equal to "x" minus left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "X" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis less than or equal to negative StartFraction, 2 plus StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot , EndFraction , right bracey−2+3YA−3=−1−32−4+3323≤x−2+3XA−3≤−2+323
24
Expression 25: "A" equals left bracket, 0 , ... , "W" "H" minus 1 , right bracketA=0,...,WH−1
25
Expression 26: "X" left parenthesis, "n" , right parenthesis equals mod left parenthesis, "n" , "W" , right parenthesisXn=modn,W
26
Expression 27: "Y" left parenthesis, "n" , right parenthesis equals floor left parenthesis, StartFraction, "n" Over "W" , EndFraction , right parenthesisYn=floornW
27
Expression 28: "W" equals 7W=7
28
Expression 29: "H" equals 7H=7
29
Expression 30: left parenthesis, left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "X" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis , left parenthesis, 2 plus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "Y" left parenthesis, "A" , right parenthesis minus 3 , right parenthesis , right parenthesis2+3XA−3,2+3YA−3