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Question:

Tiling the plane? need help asap?

How do you show how to tile the plane?For example, if you use ‘+‘ (the plus shape)Do you merge/group the pluses ‘+‘ together to form a ‘+‘ plus shape again?Is that what tiling the plane means?Also, I am asked to determine all the basic rigid symmetries of this tiling (i.e. all shifts, flips and rotations). Do all three cases arise? No right? Just the shifts one?Then they also ask: Does this tiling have any symmetries of scale? (My question: How would you know this?)Thanks guys!Appreciate all your help.

Answer:

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BA AAAB BABBBA <---Top of A cross is right of middle of B cross! ABABAAAB BAAABABB BBABBBAB This pattern continues in both directions indefinitely. This forms a staircase which is two letters wide and one letter drop at each step. these can fit together perfectly. What I described has a natural 2 right-1 down pattern (from center of cross to center of cross) and a 1 right- 2 up pattern. The slopes of -1/2 versus 2 are perpendicular to one another, but do not give reflective possibilities (I don't think). Rotations by 90 degrees and slides do occur and I think these are all possibilities. The rotations can be centered at several points.

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