This question may be rather trivial, but I don't understand if a regular tetrahedron is orthocentric.
In Wikipedia's "Orthocentric tetrahedron" entry, it is said that:
"[A]n orthocentric tetrahedron is a tetrahedron where all three pairs of opposite edges are perpendicular."
And then, in the same article it is said that:
"In an orthocentric tetrahedron the four altitudes are concurrent."
In the case of a regular tetrahedron, the four altitudes are concurrent (and therefore it has a orthocenter), though three pairs of opposite edges are not perpendicular.
I don't know which of these two criteria is defining in terms of calling a tetrahedron orthocentric. From the article, it seems like a regular tetrahedron is not orthocentric, but it would sound strange to me since it is one of just two tetrahedrons with actual orthocenters.
Maybe I don't understand something - English is not my first language.