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