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If a dice has 3 on the top, right back 6, right front 2, bottom 4, left front 1, left back 5 and is rotated by +180 about the z axis and +90 about the x axis, how many dots does each face have after the rotation?

  • Math-geometry - ,

    You talk about front, bottom, left

    then you mention x axis, z axis.

    Where are the axis?

  • Math-geometry - ,

    the z axis is top/ bottom, the x/y axis is right/ left

  • Math-geometry - ,

    180° about z takes (x,y,z) -> (-x,-y,z)
    90° about x takes (x,y,z) -> (x,z,-y)

    so, your two rotations take (x,y,z) -> (-x,z,y)

    So, figure where the spots start out, and apply the rotations.

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