Properties of Isosceles Tetrahedra

a

1.2

b

1

c

1

2D/3D

net	polyhedron

show labels

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.

External Links

Isosceles Tetrahedron (Wolfram MathWorld)

Disphenoid (Wolfram MathWorld)

Cayley–Menger Determinant (Wolfram MathWorld)

Tetrahedron (Wolfram MathWorld)

Linked Sliders

Permanent Citation

Izidor Hafner

"Properties of Isosceles Tetrahedra"
http://demonstrations.wolfram.com/PropertiesOfIsoscelesTetrahedra/
Wolfram Demonstrations Project
Published: April 24, 2017