# Rumple

## by Jo Hoffhacker (not Holly's grandmothers)

# *333 (ignoring color)

# Analysis of Rumple

#### KEY:

1) red segments represent reflection mirrors

2) light green segments represent glide mirrors that are not reflection mirrors

3) dark blue segments represent translation generators

4) dark green segments represent shortest glide vectors that are not translation
generators

5) yellow points represent cyclic centers

6) light blue points represent dihedral centers

7) fundamental region is shaded pink

8) quilt block is shaded yellow

####

####

####

####

####

####

####

####

#### Symmetries present: reflection,
glide reflection, rotation, translation

#### Description of symmetries (in pieces): Because
of the colors of the non-blue equilateral triangles, technically the pattern
is assymetrical. However, if we ignore the patterning and consider all of
the non-blue triangles to be the same, then the pattern is *333. There are
3 directions of mirrors that are also glide mirrors. At the intersection of
any 3 of these mirrors are dihedral 3-fold centers. The translation generators
are as shown (note that the lattice is hexagonal.) The shortest glide vectors
are twice the shortest translation vectors (CHECK) and a sample in each direction
is shown.

#### Description of fundamental region:
a SMALL equilateral triangle whose sides are
mirrors and vertices are 3-fold centers. No mirrors pass through the fundamental
region, so it "straddles" a blue and non-blue triangle.

#### Description of symmetries in a block:This
quilt was made with the equilateral triangles pieces, not with a block. Jo
said that she stitched the triangles together into rows before stitching the
rows together.