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Cuboid
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<p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a cuboid is a <a href="/facts/Hexahedron/UzruYxzd">hexahedron</a> with <a href="/facts/Quadrilateral/QCGqrkp2">quadrilateral</a> faces, meaning it is a <a href="/facts/Polyhedron/UC0p9FTF">polyhedron</a> with six <a href="/facts/Face_(geometry)/T2E6BTU4">faces</a>; it has eight <a href="/facts/Vertex_(geometry)/ID3cea9z">vertices</a> and twelve <a href="/facts/Edge_(geometry)/3lFN6sEz">edges</a>. A <i><a href="/facts/Rectangular_cuboid/eLLKX4rh">rectangular cuboid</a></i> (sometimes also called a "cuboid") has all <a href="/facts/Right_angle/psaslRq7">right angles</a> and equal opposite <a href="/facts/Rectangular/mdLfIGKA">rectangular</a> faces. Etymologically, "cuboid" means "like a <a href="/facts/Cube/65lUaAqN">cube</a>", in the sense of a <a href="/facts/Convex_polyhedron/2pRHcRgC">convex</a> solid which can be transformed into a cube (by adjusting the lengths of its edges and the <a href="/facts/Dihedral_angle/C9WEJsuS">angles</a> between its adjacent faces). A cuboid is a convex polyhedron whose <a href="/facts/Polyhedral_graph/IKPCDH6r">polyhedral graph</a> is the same as that of a cube. </p><p>General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a <a href="/facts/Cube/65lUaAqN">cube</a>, with six <a href="/facts/Square/JHJeMvmL">square</a> faces and adjacent faces meeting at right angles. Along with the rectangular cuboids, <i><a href="/facts/Parallelepiped/Qn7cDgSr">parallelepiped</a></i> is a cuboid with six <a href="/facts/Parallelogram/DRuktq60">parallelogram</a>. <i><a href="/facts/Rhombohedron/S7XSr6Yu">Rhombohedron</a></i> is a cuboid with six <a href="/facts/Rhombus/T4pU50GF">rhombus</a> faces. A <i><a href="/facts/Square_frustum/TEfLWynX">square frustum</a></i> is a frustum with a square base, but the rest of its faces are quadrilaterals; the square frustum is formed by <a href="/facts/Truncation_(geometry)/DYb589Je">truncating</a> the <a href="/facts/Apex_(geometry)/SrMxmHJk">apex</a> of a <a href="/facts/Square_pyramid/wDetDohM">square pyramid</a>. In attempting to classify cuboids by their symmetries, Robertson (1983) found that there were at least 22 different cases, "of which only about half are familiar in the shapes of everyday objects". </p><p>There exist quadrilateral-faced hexahedra which are non-<a href="/facts/Convex_polyhedron/2pRHcRgC">convex</a>. </p> Some notable cuboids(<a href="/facts/Quadrilateral/QCGqrkp2">quadrilateral</a>-faced convex <a href="/facts/Hexahedra/UzruYxzd">hexahedra</a> • 8 vertices and 12 edges each)<table><tbody><tr><th>Image</th><th>Name</th><th>Faces</th><th>Symmetry group</th></tr><tr><td></td><td><a href="/facts/Cube/65lUaAqN">Cube</a></td><td>6 <a href="/facts/Congruence_(geometry)/2tKJ6AhB">congruent</a> squares</td><td>Oh, [4,3], (*432)order 48</td></tr><tr><td></td><td><a href="/facts/Trigonal_trapezohedron/w5qPRnR3">Trigonal trapezohedron</a></td><td>6 congruent <a href="/facts/Rhombus/T4pU50GF">rhombi</a></td><td>D3d, [2+,6], (2*3)order 12</td></tr><tr><td></td><td><a href="/facts/Rectangular_cuboid/eLLKX4rh">Rectangular cuboid</a></td><td>3 pairs of <a href="/facts/Rectangle/mdLfIGKA">rectangles</a></td><td rowspan="2">D2h, [2,2], (*222)order 8</td></tr><tr><td></td><td>Right rhombic <a href="/facts/Prism_(geometry)/baIRRkCy">prism</a></td><td>1 pair of rhombi,4 congruent <a href="/facts/Square_(geometry)/JHJeMvmL">squares</a></td></tr><tr><td></td><td>Right square <a href="/facts/Frustum/TEfLWynX">frustum</a></td><td>2 non-congruent squares,4 congruent <a href="/facts/Isosceles_trapezoid/Izn5AA4p">isosceles trapezoids</a></td><td>C4v, [4], (*44)order 8</td></tr><tr><td></td><td>Twisted trigonal <a href="/facts/Trapezohedron/8QpjlnXe">trapezohedron</a></td><td>6 congruent quadrilaterals</td><td>D3, [2,3]+, (223)order 6</td></tr><tr><td></td><td>Right isosceles-trapezoidal prism</td><td>1 pair of isosceles trapezoids;1, 2 or 3 (congruent) square(s)</td><td>?, ?, ?order 4</td></tr><tr><td></td><td><a href="/facts/Rhombohedron/S7XSr6Yu">Rhombohedron</a></td><td>3 pairs of rhombi</td><td rowspan="2">Ci, [2+,2+], (×)order 2</td></tr><tr><td></td><td><a href="/facts/Parallelepiped/Qn7cDgSr">Parallelepiped</a></td><td>3 pairs of <a href="/facts/Parallelogram/DRuktq60">parallelograms</a></td></tr></tbody></table>