Symmetries of the Octahedron

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rotations

mirrors

both

all symmetries

number of given faces

2

3

4

5

create new example

show solution

1	2	3	4	5	6	7	8
8					3	4

The sum of the numbers on opposite vertices of an octahedral die equals 9. Symmetry operations on the die move some faces into their original positions, as shown in the table. Rotate the image to see other faces.

External Links

Octahedral Group (Wolfram MathWorld)

Octahedral Rotational Symmetry Types

Icosahedral Group (Wolfram MathWorld)

Icosahedral Group Polyhedra

Icosahedral Rotational Symmetry Types

Generating 3D Figures with a Given Symmetry Group

Permanent Citation

Izidor Hafner

"Symmetries of the Octahedron"
http://demonstrations.wolfram.com/SymmetriesOfTheOctahedron/
Wolfram Demonstrations Project
Published: March 24, 2022