The geometric shape that would almost match those characteristics is a triangular pyramid, as it would have four faces rather than three
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It is a cuboid which has 6 faces, 12 edges and 8 vertices
A cube is a geometric shape which has 6 faces and 8 vertices ie .2 more vertices than faces
A shoe box can be in the shape of a cuboid that has 6 faces, 12 edges and 8 vertices
A sphere has no faces, edges, or vertices.
The geometric shape that has 1 square face and 4 triangular faces is a pyramid. A pyramid also has five vertices and eight edges. The square acts as the base for the shape on which it sits.