17 Types of Symmetry

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17 Types of Symmetry	17 images
tree :: Geometry > 17 Types of Symmetry

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A polyhedron can have one of 17 types of symmetry. These are the collections of ways in which a polyhedron can be repositioned without being able to distinguish the new position from the original position.

Some of the symmetry types have an infinite number of members. The n in the symmetry type is replaced with an integer to give the particular symmetry.

The images and models have been produced with a polyhedral kaleidoscope program poly_kscope. An asymetric arrow is repeated in the given symmetry pattern to produce each model. The number of arrows is then equal to the number of symmetries (possible congruent repositionings) of the model.

The models can be viewed with JavaView which allows them to be rotated and seen from different angles. This is a new feature on the site and is activated with JavaScript code which may yet require some tuning to work on different browsers.

Image List

C1 Symmetry

Med Lrg

Description :

C1 symmetry - no symmetry.

view model with JavaView.

Click on one of the size names above to enlarge this image

Ci Symmetry

Med Lrg

Description :

Ci symmetry - inversion symmetry only.

view model with JavaView.

Cs Symmetry

Med Lrg

Description :

Cs symmetry - reflection symmetry only.

view model with JavaView.

Cn Symmetry

Med Lrg

Description :

Cn symmetry - cyclic rotational symmetry only. The model shown has C5 symmetry with a vertical 5-fold axis of symmetry.

view model with JavaView.

Cnv Symmetry

Med Lrg

Description :

Cnv symmetry - cyclic rotational symmetry with reflection symmetry in a vertival mirror. The model shown has C5v symmetry with a vertical 5-fold axis of symmetry.

view model with JavaView.

Cnh Symmetry

Med Lrg

Description :

Cnh symmetry - cyclic rotational symmetry with reflection symmetry in a horizontal mirror. The model shown has C5h symmetry with a vertical 5-fold axis of symmetry.

view model with JavaView.

Sn Symmetry

Med Lrg

Description :

Sn symmetry - cyclic rotational (n/2-fold) with reflection symmetry in a horizontal mirror. The model shown has S6 symmetry with a vertical 3-fold axis of symmetry.

view model with JavaView.

Dn Symmetry

Med Lrg

Description :

Dn symmetry - dihedral rotational symmetry only. The model shown has D5 symmetry with a vertical 5-fold axis of symmetry.

view model with JavaView.

Dnv Symmetry

Med Lrg

Description :

Dnv symmetry - dihedral rotational symmetry with reflection symmetry in a vertival mirror. The model shown has D5v symmetry with a vertical 5-fold axis of symmetry.

view model with JavaView.

Dnh Symmetry

Med Lrg

Description :

Dnh symmetry - dihedral rotational symmetry with reflection symmetry in a horizontal mirror. The model shown has D5h symmetry with a vertical 5-fold axis of symmetry.

view model with JavaView.