 (Expectation, by Gustav Klimt)
Homothety
In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point A called the origin.
Two figures are homothetic if they are related by an expansion or geometric contraction; this means that they lie in the same plane and corresponding sides are parallel; such figures have connectors of corresponding points which are concurrent at a point known as the homothetic center.
The number c by which distances are multiplied is called the dilation factor or similitude ratio. Such a transformation is also called an enlargement.
More generally c can be negative; in that case it not only multiplies all distances by |c| , but also inverts all points with respect to the fixed point.
A homothety is an affine transformation (if the fixed point is the origin: a linear transformation) and also a similarity transformation. It multiplies all distances by |c| , all surface areas by c2, etc.
In the above figure, O is the homothetic center of the homothetic figures ABCDE and A’B’C’D’E’.
Solid geometric figures
Polyhedra
(A polyhedron is a solid with no curved surfaces or edges. All faces are polygons and all edges are line segments. The corner points where three or more adjacent sides meet are called vertices).
Prisms:
   
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