A polyhedron with 76 faces is called a heptahexahedron ... I think. (It may be also be called a heptacontahexahedron) Why a heptahexahedron? Well ... people have made all the common and most of the not-so-common polyhedra on Scratch so I chose an unusual polyhedron just to be first. :) Anyway, this heptahexahedron has 76 triangular faces, 40 vertices and 114 edges.
Huge thanks to @TheLogFather for his "Faster Triangle Filler" https://scratch.mit.edu/projects/24828481/ Theory to rotate a 3D object: https://en.wikipedia.org/wiki/Rotation_matrix