**Problem : **
Using your knowledge of concentric circles come up
with a definition for concentric spheres.

Concentric spheres are spheres that share a common center.

**Problem : **
Which of the regular polyhedra are prisms?

The only regular polyhedron that is a prism is a cube.

**Problem : **
Triangles can be combined to form any
polygon. Is there a geometric solid that can
be
combined to form any of the regular polyhedra?

Yes. A number of regular pyramids can be combined to form any of the
regular
polyhedra. The regular pyramids would all be
congruent. The bases of the
regular
pyramids would be the

*faces* of the regular polyhedra. All

*n*
regular
pyramids (for an

*n*-sided regular polyhedron) would share a common
vertex: the point from which all
vertices of the regular polyhedron are equidistant. Such regular pyramids,
united with
their interiors, would form a geometric solid that would be congruent to a
regular
polyhedron and its interior.

**Problem : **
Based on your knowledge of plane geometry, develop definitions for polyhedra
inscribed
in a sphere and polyhedra circumscribed about a
sphere.

A polyhedron inscribed in a sphere touches the sphere with all of its
vertices. A polyhedron circumscribed about a sphere has faces that are all
tangent
(intersect at one point) to the sphere.

**Problem : **
Devise a definition of the center of a regular polyhedron.

The point from which all the vertices of the polyhedron are equidistant