Inscribed and Circumscribed Spheres of a Tetrahedron

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A tetrahedron is defined by the six edge lengths ,
,
,
,
,
. The inscribed and circumscribed spheres of the tetrahedron are constructed. The incenter is shown as a blue dot, and the circumcenter is a red dot. When do the centers of the inscribed and circumscribed spheres coincide?
Contributed by: Izidor Hafner (April 2017)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The centers of the inscribed and circumscribed spheres coincide if and only if the tetrahedron is isohedral (when all its faces are the same) or an isosceles tetrahedron [1, p. 103, pp. 118–120].
Reference
[1] V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.
Permanent Citation
"Inscribed and Circumscribed Spheres of a Tetrahedron"
http://demonstrations.wolfram.com/InscribedAndCircumscribedSpheresOfATetrahedron/
Wolfram Demonstrations Project
Published: April 25 2017