tangent spheres

From: Calvin <crice5@xxxxxxxxxxxxxx>
Date: Fri, 7 Dec 2007 19:23:13 -0800 (PST)

Consider three tangent spheres of radius 1. The three tangent points
form an
equilateral triangle, obviously. Place a fourth sphere of radius 1
such that it
is tangent to the original three. This creates three more tangent
points,
obviously. The four centers of the spheres form a tetrahedron,
obviously.

What is the volume of the tetrahedron? What is the shape of the space
formed by the six tangent points? What is its volume?
.

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