Frieze Group

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2014-10-14 22:07

In collections MTH 595 Book

This example demonstrates the symmetry of the Frieze group. It involves core mathematical concepts such as translation and mirror transformations. Using GeoGebra commands like Line and Mirror, you can construct a Frieze group pattern. Suitable for middle school and above students to learn geometric transformations.

GeoGebra Commands & Parameters

Line(A, B) → a
Line(C, a) → b
Mirror(D, a) → D'
Mirror(D, b) → D'_1
Mirror(a, b) → a'
Mirror(b, a) → b'
Mirror(D', b) → D''
Mirror(a', a) → a''
Mirror(b', b) → b''
Mirror(b'', a) → b'''
Mirror(b''', a) → c
Mirror(D, b') → D'_2
Mirror(D', b') → D''_1
Mirror(D'_1, b'') → E
Mirror(D'', b'') → D'''
Mirror(a', b'') → a''_1
Mirror(b'', a''_1) → b'''_1
Mirror(a''_1, b'''_1) → d
Mirror(b'''_1, d) → e
Mirror(E, b'''_1) → E'
Mirror(D''', b'''_1) → F
Mirror(E', e) → E''
Mirror(F, e) → F'
Mirror(d, e) → d'
Mirror(e, d') → e'
Mirror(a'', b''') → a'''
Mirror(b''', a''') → f
Mirror(a''', f) → g
Mirror(d', e') → d''
Mirror(e', d'') → e''
Mirror(d'', e'') → d'''
Mirror(E'', e') → E'''
Mirror(F', e') → F''
Mirror(E''', e'') → G
Mirror(F'', e'') → F'''
Mirror(D'_2, b''') → H
Mirror(D''_1, b''') → I
Mirror(H, f) → H'
Mirror(I, f) → I'

AI Drawing Prompt Reference

Create a Frieze group pattern with horizontal translation and mirror transformations. Start by drawing two parallel lines a and b, then take a point D on line a and perform mirror transformations with respect to a and b to get points D', D'', and so on. Next, take point D' on line b and perform mirror transformations with respect to a and b to get points D''_1, and continue with mirror transformations to complete the pattern.

The prompt above was compiled from the original drawing commands and is for reference only.