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Properties of Isosceles Tetrahedra

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

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

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Contributed by: Izidor Hafner (April 2017)
Open content licensed under CC BY-NC-SA

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