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- Which letters of the alphabet written in upper case block style have asymmetry group with four elements? Describe the four symmetries.there are 3 square decimeters. 8. a) which transformation would make the 2 become a 5. 25 b) the digit "2" has how many rotational symmetries a its center. 2Find the number of ways to colour faces of a cube using at most k colors, up to the group of symmetries we get using rotations AND reflections
- (ii) Following the example on symmetries of the equilateral triangle from the written notes, list all the symmetries of the shape above and the associated permutations of {1,2, 3, 4}.Which figure has the greatest order of rotational symmetry? OFor the set of numbers 1 Less than or equal to x less than or equal to 9, list the ones that have reflection symmetry. Then list the ones that have rotational symmetry. Draw, for both symmetries, them to the right.
- (iv) How many permutations of the set {1,2,3, 4} do not correspond to symmetries of the rectangle? Justify your answer.How many ways are there to put five beads on a necklace if there are eight distinct beads to choose from, and rotations and reflections of the necklace are considered the same?Determine all the symmetries of the figures below. Draw any lines of symmetry. Below the figure, list any other kinds of symmetry (rotational, translational) the figure has. If the figure has rotational symmetry, tell how many different positions could be shown (e.g.does it have 2-fold? 3-fold?).
- The operation between two symmetries can be thought of as a composition,with the result of the first symmetry being the starting point for thesecond symmetry. The composition symbol, °, will denote the operation between two symmetries. For example, the operation R180 ° MH would mean that, starting from the rightmost operation, the symmetry MH would be applied to the original figure first, with the result then being followed by R180, a counterclockwise rotation by 180 degrees. The result of the composition is equivalent to symmetry MV applied to the original figure (Figure 5), so we can express the final result as R180 ° MH = MV. Complete the following Cayley table: ° Apply First Apply Second ° 1 R180 MH MV 1 R180 MV MH MV The symmetries will be denoted by S, i.e., S = {1, R180, MH, MV}.ii. Explain why the system (S, °) is closed.iii. Provide at least three examples that can be used to conjecture that the system (S, °) is associative. iv.…Question 16 livery-ui/v3.19.3/assessment/page/16?token=087366c9bb8ba9bf01f2ee035faa85ac Winnie says that all objects with rotational symmetry also have point symmetry. Henrico says that all objects with point symmetry also have rotational symmetry. Who is correct? OA) Winnie is correct. OB) Henrico is correct. OC) Both Winnie and Henrico are correct. OD) Neither Winnie nor Henrico are correct.Determine the kind of symmetries found in the wallpaper pattern shown below not including the identity. A grid of capital Bs extends forever in all directions. A. translations and horizontal reflections only B.translations and 180° rotations only C. translations only D. translations and vertical reflections only E. none of the above