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The Menger sponge is a fractal which is the three-dimensional analog of the Sierpiński carpet. The nth iteration of the Menger sponge is implemented in the Wolfram Language ...

There are two definitions of a metacyclic group. 1. A metacyclic group is a group G such that both its commutator subgroup G^' and the quotient group G/G^' are cyclic (Rose ...

The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...

A solid of revolution is a solid enclosing the surface of revolution obtained by rotating a 1-dimensional curve, line, etc. about an axis. A portion of a solid of revolution ...

The tetrix is the three-dimensional analog of the Sierpiński sieve illustrated above, also called the Sierpiński sponge or Sierpiński tetrahedron. The nth iteration of the ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. ...