Disphenoid
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Disphenoid is a tetrahedron whose four faces are congruent acute-angled triangles.
Main
a) A tetrahedron is a disphenoid iff
b) A tetrahedron is a disphenoid iff its circumscribed parallelepiped is right-angled.
c) Let
The squares of the lengths of sides its circumscribed parallelepiped and the bimedians are:
The circumscribed sphere has radius (the circumradius):
The volume of a disphenoid is:
Each height of disphenoid
is
the inscribed sphere has radius: