Symmetry

In a previous unit, you explored the different symmetries of two-dimensional objects: reflectional and rotational. Three-dimensional shapes may also have these symmetries as well.

A three-dimensional shape has reflectional symmetry when there is a plane of symmetry that appears to "cut" the solid into two congruent parts.  Reflectional symmetry is also known as mirror symmetry or bilateral symmetry.  The figures below show two examples of reflectional symmetry of a cube. There are many more planes of symmetry for this solid.

reflect symm

A three-dimensional shape has rotational symmetry when there is a line through the solid acting as an axis that the solid can rotate around to fit onto itself after a turn of less than 360°.  The figure below shows two different axes of symmetry for this solid.

rotation

 

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