Each response is on an equilateral triangle face, so the die inside must be either a tetrahedron, octahedron, or a icosahedron (d4, d8 or d20). There are no other regular polyhedrons composed of equilateral triangles.
Doesn't take too many attempts to see more than 4 answers, so it can't be the tetrahedron. It might take a large number of attempts to get the 9th unique response, but if you look carefully you can sort of see the adjacent faces while the die settles. Not well enough to read, but well enough to get an idea of the angle between the faces. Too shallow to be an octahedron, so it must be a dodecahedron.