Day 8 : Make  Figures with 7 types of Strip Pattern Symmetry

by Jongsuk Keum

Goal
Students explore 7 types of strip pattern, make the multiplication table, and make figures for the strip pattern using GSP.
Multiplication table for Strip Pattern
A detailed multiplication table for the types of isometries which occur as symmetries of strip pattern. Let L be the center line of a strip pattern. Make a table for the types
• I = identity
• T = translation with vector parallel to L, T not the identity
• R = rotation with center on L and angle 180 degrees
• V = reflection with "vertical" mirror, i.e. mirror perpendicular to L
• H = reflection with "horizontal" mirror, i.e. mirror L
• G = glide reflection with mirror L, G not equal to H

 I T R V H G I I T R V H G T T T,I R V G H,G R R R T,I H,G V V V V V H,G T,I R R H H G V R I T G G G,H V R T T,I

Seven types of strip pattern

T, TR, TV, TG, THG, TRVG, TRVHG

Conway's names for strip pattern

1. Hop ( T )

2. Spinning Hop ( TR )

3. Sidle ( TV )

4. Step ( TG )

5. Jump ( THG )

6. Spinning Sidle ( TRVG )

7. Spinning Jump ( TRVGH )

Homework

Make figures of 7 types of Strip Pattern symmetry using GSP