Question

please help me with #5

thank you :)

5. The operation table for a group G = {e, .g.h} is given. The group G describes the symmetries of one of the three objects (A) rectangle, (B) ghost, or (C) pinwheel. olle f g hl ele f g h ss g h el 99 hef (A) (B) Which object is G the group of symmetries for? Circle your answer and give specific reasons why G cannot be the symmetry group of the other two objects.

Answer 1

solution Given dala from the question. The group has order 4 (4 element, erf, og ands) ere e is density, g has order 2, f and h have order 4. The symmetry group of the reclongle which has solation by o solation by 1806 Horizontal reflection and vertical reflection as the - symmetries. 7 The rotation by leo, and the two reflections all have coder 2. .. So the sectongle is not the answer. 7 on the other hand, the middle figure has o degree solution as the only solutional symmetry and only vertical symmetry. So, its symmetry group has order 2. And the right most figure has solation by 0, 90, 180, 210 degree Strometrics 180 degree roolution has order 2 and other two roolations have order 4. This, the correct option fs (c) the pinwheel.