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A regular hexagonal room has 6 rotational symmetries (rotational symmetry of order six) and 4 reflection symmetries.

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A regular hexagonal room has 6 rotational symmetries (rotational symmetry of order six) and 4 reflection symmetries.

(a) False

(b) True

The question was asked by my school teacher while I was bunking the class.

Origin of the question is Circular, Semicircular, Hexagonal & Half Hexagonal Rooms topic in section Methods of Building Estimate & Estimate of Building of Civil Engineering Drawing

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Right option is (a) False

Easy explanation: A regular hexagonal room has 6 rotational symmetries (rotational symmetry of order six) and 6 reflection symmetries (six lines of symmetry), making up the dihedral group D6. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side.

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