You kick Phill in the head
A cuboctahedron has 12 vertices.
A cuboctahedron has 24 edges.
A cuboctahedron has 14 faces: 8 triangles and 6 squares.
Cuboctahedron
cuboctahedron
Cheese is nice on crackers.
It has 14 faces, 24 edges and 12 vertices
A cantellated regular tetrahedron, in the form of a regular cuboctahedron, has 14 faces (8 triangular, and 6 square), 24 edges and 12 vertices.
A rhombic dodecahedron is a 3-D shape (polyhedron) that has 12 rhombic faces, 24 edges (sides), and 14 vertices (points). Its dual is a cuboctahedron. If you wanted to try by yourself, get a transparent model and start counting!
There are very many possible shapes: a square based pyramid a triangular prism a square anti-prism a cuboctahedron a rhombicuboctahedron and possibly more. See link for images.
I am thinking the strongest 3-D would be a sphere. This is because of the repetition of the arc. Depending of what the application of the 3-D shape is, different polygons should be considered. If you are thinking strictly in mathematical terms, my answer remains sphere. Other shapes to consider: The triangular pyramid The pyramid (square base) The right triangle cone (circular base) The cuboctahedron The cuboctahedron is six square faces and eight triangular faces. My reasons for including it in stronger 3-D shapes without proof of any kind is: there are triangles confining squares thus leading to limits on distortion of the squares to other shapes such as rectangles or trapezoids. In addition there is a large potential for shock distribution over the many faces because the near spherical appearance and construct.
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