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There are an infinite number of possible solutions.
A tetrahedron and icosahedron are regular shapes. Then there is the triangular prism.
A cuboid with one vertex cut off, a cube with 2 vertices cut off, 3 vertices etc. In fact, cutting off the vertex of any polyhedron in which three sides (faces) meet at the vertex will give a new triangular face.
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Earn +20 ptsQ: Which polyhedron has a trangular base?
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