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A snub cube has 6 square faces and 32 triangular faces. Allowing for only rotations of the object (no mirror reflections), how many elements are there in the group of symmetries of this object. Easiest to show in permutations of 32 triangles.

I am having trouble finding the elements of this group, the order of the group is said to be 24 and the number symmetries is equivalent to the number of diagonals in a cube, 12. I have the net of the snub cube, trying to see if i can get one of the rotational colourings listed.

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    $\begingroup$ There are 6 faces that can be on top, and 4 rotations for whatever the top face is... 24 $\endgroup$ – Doug M Nov 29 '17 at 1:55
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    $\begingroup$ @DougM Well, 6 faces provided you want one of the square faces to be on top, but we can assume that. $\endgroup$ – Misha Lavrov Nov 29 '17 at 2:07
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    $\begingroup$ List the rotations of the simple cube, that would be it. $\endgroup$ – Ivan Neretin Nov 29 '17 at 6:23

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