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The solid figure that has 4 flat surfaces that are triangles is a tetrahedron. A tetrahedron is a polyhedron with four triangular faces, six straight edges, and four vertex corners. Each of the four faces of a tetrahedron is an equilateral triangle, making it a regular polyhedron.
They have flat surfaces
Slate breaks along smooth flat surfaces because of its foliated structure, consisting of fine-grained minerals aligned parallel to the direction of pressure during its formation. This alignment allows slate to easily split along these planes, resulting in the characteristic smooth surfaces when fractured.
Gypsum has cleavage, which means it tends to break along flat surfaces.
... because calcite has a regular arrangement of atoms.