WOLFRAM|DEMONSTRATIONS PROJECT

Generating 3D Figures with a Given Symmetry Group

​
choose group type:
I
h
O
h
T
h
I
O
T
T
d
D
n
C
n
D
nv
C
nv
D
nh
C
nh
S
2n
show (one) principal axis
show (one) mirror plane if there is one
new motif
The figure's symmetry group is
I
h
.
A symmetry of a figure is a transformation, such as a rotation, reflection, inversion, etc., that repositions the figure to be indistinguishable from the original. For example, rotating a circle about its center is a symmetry of the circle.
All the symmetries of a figure form a group called the figure's symmetry group. This Demonstration considers some figures in 3D consisting of finite sets of congruent triangles.