An isosceles tetrahedron is a nonregular tetrahedron in which each pair of opposite polyhedron edges
are equal, i.e., ,
,
and ,
so that all triangular faces are congruent. Isosceles tetrahedra are therefore isohedra.
The only way for all the faces of a general tetrahedron to have the same perimeter or to have the same area
is for them to be fully congruent, in which case the tetrahedron is isosceles.
The circumradius of an isosceles tetrahedron can be found by plugging in the volume of a general tetrahedron
into the relationship
(2)
where
is the volume and
is the area of a triangle with side lengths , , and to obtain
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