Properties of Isosceles Tetrahedra

An isosceles tetrahedron is a nonregular tetrahedron in which each pair of opposite polyhedron edges are equal; that is,

e=a

,

d=c

,

f=b

. Then all the triangular faces are congruent, so that an isosceles tetrahedron can be classified as an isohedron. An isosceles tetrahedron is also called a disphenoid.

This Demonstration shows that in an isosceles tetrahedron, the three plane angles at each vertex sum to

π

. Therefore, a net

N

of an isosceles tetrahedron is a triangle similar to the faces of the solid, and the sides of the net are twice the sides of the faces.