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Question: How to create a tetrahedron whose vertices are integers, the inscribed spherical center and the inscribed spherical radius are integers?

Question:How to create a tetrahedron whose vertices are integers, the inscribed spherical center and the inscribed spherical radius are integers?

minhthien2016 370 Maple 2018
February 02 2021
2

I know that, tetrahedron with vertices (0, 0, 0), (3, 0, 0), (0, 5, 0), (0, 0, 14) has center of insphere is  (1, 1, 1) and radius R = 1. How to create a tetrahedron whose coordinates of all vertices are integers, the inscribed spherical center and the inscribed spherical radius are integers?
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