The Stone Lions (31 page)

Abd al-Rahmid, Wazir

Ara, a girl of the harem. Daughter of the sultan

Dananir, fourth wife of the sultan

Enrique, son of the Lady Theresa

Fatima, Zoriah’s grandmother. One of the women living
in the harem

Hasan, a young boy who lives in the harem

Lady Anna, visiting woman from the north of Spain

Lady Catalina, visiting woman from the north of
Spain

Lady Theresa, visiting woman from the north of
Spain

Layla, Ara’s cousin

Maryam, Layla’s mother

Rabab, Ara’s Great Aunt, who also lives in the
harem

Sara, young girl in the harem

Sister Helena, nun from the north of Spain

Sister Mary, nun from the north of Spain

Su’ah, a Saracen slave

Suleiman, a palace slave who has risen to the job of
harem tutor

Sultan, Muhammad VII, father of Ara

Tahirah, famous Sufi mathemagician

Thana, second wife of the sultan’s brother, Abn
al-Humam

Zoriah, head wife of the sultan

Loyalty

Vigilance

Justice

Wisdom

Endurance

Reason

Strength

Prudence

Discipline

Courage

Patience

Curiosity

Band symmetry: seven symmetries that form a one-dimensional pattern
(a row or band) and seventeen wallpaper symmetries
(two-dimensional) have been used in art and architecture for almost
as long as people have created art and architecture.

Recently, three-dimensional symmetry was discovered
to be important in many areas of science; in particular,
crystallography and particle science. This book is an introduction
to band symmetry (one-dimensional symmetry).

There are seven possible band
symmetries

1.Vertical Reflection

A symmetry family with a vertical reflection. There
is no rotation and no horizontal reflection. Bilateral Symmetry is
included in this group. Two of the vertical lines are shown here
with arrows.

2. Horizontal
Reflection

A symmetry family with a horizontal reflection. There
is no rotation and no vertical reflection. The single horizontal
line is shown above.

3. Double reflection

A symmetry family that has two reflections, one over
a horizontal line and over a vertical line. It does rotate and it
looks the same upside down as right side up. The single horizontal
line plus two of many possible vertical lines of reflection are
shown above.

4. Translation

An asymmetrical shape with no reflection and no
rotation. It moves by translation or sliding. No vertical or
horizontal lines are possible.

5. Rotation

An asymmetrical object that rotates around a point.
There is no reflection. Three of the points of rotation are shown
above with dots.

6. Glide reflection

An asymmetric object with a glide. No vertical
mirror, does not rotate. The object glides (the triangle shows the
first glide) and then reflects. The horizontal line is shown as a
single glide.

7. Glide with a vertical
mirror

A symmetric object (the vertical mirror) that glides.
It also can be seen to rotate. The object reflects, creating the
double triangle, then it glides (as shown by the double triangle)
and then it reflects. The horizontal line is shown. This symmetry
can also rotate. Two of the points of rotation are shown with
dots.

And Four Motions

Reflection (mirror or flip), the image flips over a
horizontal or vertical line

Rotation, the image turns around a fixed point

Translation (Slide), the image moves along the row
one space

Glide reflection, the image moves along the row one
space and then flips over a horizontal line