Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The an...

Question

Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is:

A. 30°
B. 60°
C. 45°
D. 90°

Accepted Answer

The dihedral angle of a regular tetrahedron is arccos(1/3) ≈ 70.53°. None of the given options (30°, 60°, 45°, 90°) match this value. The question is marked excluded (X) in the official answer key. Four equilateral triangles joined edge-to-edge form a regular tetrahedron — the simplest Platonic solid. The dihedral angle is the angle measured between two adjacent faces along their shared edge. For a regular tetrahedron this angle is arccos(1/3) ≈ 70.53°, which is none of the given options, hence the question is marked excluded (X) in the official answer key.

Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is: A. 30° B. 60° C. 45° D. 90°