Symmetries of the Dodecahedron

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rotations

mirrors

both

all symmetries

number of given faces

2

3

4

5

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show solution

1	2	3	4	5	6	7	8	9	10	11	12
	1								4	12

The sum of the numbers on opposite faces of a dodecahedral die equals 13. 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

Dodecahedron (Wolfram MathWorld)

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 Dodecahedron"
http://demonstrations.wolfram.com/SymmetriesOfTheDodecahedron/
Wolfram Demonstrations Project
Published: March 23, 2022