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Student Activity: Geometry "Rocks"
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Tony Smith, Wandering Rocks, 1967

Look carefully at Wandering Rocks to see if there is a pattern in the polygons that make up the faces.

Is there a relationship between the size and shapes of the "rocks"?
Tony Smith, Wandering Rocks, 1967


Faces Vertices
blue=
yellow=
red=
purple=
green=
Check Answers

If each rock ends with a flat side on the ground and there are no extra planes on the unseen side, how many total faces and vertices does each rock have?
Assume the "purple" rock is topped with a four-sided pyramid and it has two hidden faces, but there is only one hidden face on each of the other rocks.

Two of the rocks have been filled in for you. View a larger image of Wandering Rocks.

Don't forget to count the face lying on the ground!

How many edges?


Edges
red=
purple=
blue=
yellow=
green=
Check Answers

In 1751 Leonard Euler wrote a formula revealing the relationship between edges (E), faces (F), and vertices (V).

Now that we have the values for the faces (F) and the vertices (V), use Euler's formula to calculate the number of edges (E) in each rock

V - E + F = 2

Now study the rocks to select your answers to the following questions:

  1. Which "rocks" have the same number of faces?
    the blue and yellow rocks the purple and red rocks the red and yellow rocks

  2. Which one contains no triangles?
    the yellow rock the purple rock the red rock

  3. Which contain exactly two triangles?
    the yellow and green rocks the purple and red rocks the blue and green rocks

  4. What percent of the "rocks" have more than one face parallel to the ground?
    3/5 = 66% 2/5 = 40% 1/5 = 20%

What are the relationships between the sizes and the shapes of the rocks?

With one exception, all rocks have faces with a combination of triangles and quadrilaterals (either parallelograms or trapezoids or both).

Three rocks are the same height: 28 inches; the other two are 46 inches high. Are these relationships important to the balance or harmony of Wandering Rocks?

Rocks or Prisms?

Smith's Wandering Rocks are all polyhedra. Some are also prisms, and some are antiprisms. A prism has two equal and parallel faces joined by parallelograms.

Which rock is a prism?

the red rock
 the purple rock
 the blue rock
 the yellow rock
 the green rock

An antiprism also has two equal and parallel faces, but they are joined by triangles.

Is there an antiprism among the rocks?

yes no




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