The affine subspaces are " model " surfaces & mdash; they are the simplest surfaces in "'R "'3, and are homogeneous under the Euclidean group of the plane, hence they are " Klein geometries " in the sense of Felix Klein's Erlangen programme.
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Discrete symmetry groups come in three types : ( 1 ) finite "'point groups "', which include only rotations, reflections, inversion and rotoinversion they are just the finite subgroups of O ( " n " ), ( 2 ) infinite "'categorization of subgroups of the Euclidean group corresponds a categorization of symmetry groups.
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