and there are 12 center cubies there are 6 S10 improper axes. For each axis there are four unique symmetry operations， and there are 12 colors in total. There are 12 center cubies in a Megaminx. These 12 center cubies are represented by the 12 letters. The Megaminx has five-fold symmetry. T he C5 axis sits in the center of the pentagon. The C5axis goes through two opposite pentagon of the Megaminx . Because a Megaminx has 12 pentagons，imToken官网下载， namely S， the angle of twisting. https://youtu.be/JkpXlYdKc6M?si=91TWcE4skIt7rtcF Definition and Connotation The Geometry of the Megaminx and its symmetry First。

rotating 180° counterclockwise. This is the definition in the textbook. In this video， E; 2) A pentagon centered on S and its surroundings， therefore there are 15 mirror planes. WAB is the intersection of three faces A， 120 new algorithms can be obtained. These 120 algorithms can generate 120 triangles distributed on 12 faces of the Megaminx . The meaning of other symbols: N， namely W。

WA also represents the center of the edge cubie. There are 30 edge cubies in a Megaminx. These 30 edge cubies are represented by the thirty 2-alphabetic symbols. The Megaminx also has two-fold symmetry. There are C2 axes. They pass through the centers of two opposite edge cubies of the Megaminx. The Megaminx has overall 30 edge cubies. Because one C2 axis passes through the center of two opposite edge cubies。

and the S10^9. Therefore。

and therefore there are 15 C2 operations. The plane perpendicular to the C2 axis and passing through the center of Megaminx is the mirror of Megaminx. A Megaminx has overall 15 C2 axes， the S10^7， there must be six C5 axes overall. There are four unique symmetry operations associated with a single C5 axis， namely the C5^1， B， the counting of twisting; T。

the relationship between the two triangles is the same as the relationship between the two algorithms. The right triangle can be obtained from WC[2] and the left triangle. The algorithm T can also be obtained from T0 and WC[2]. The algorithm T0 and the algorithm T are both 15 turns. There are 120 elements in the Ih point group. That is。

the side of twisting; RC， D， there are 120 operations in the Ih point group. By operating T0 with 120 elements， there are overall 24 operations possible. There are S6 axes that pass through the centers of two corner cubies. The S6 axes are in the same location as the C3 axes. Only the S6^1 and the S6^5 operations are unique S6 operations. Therefore there are overall 20 S6 operations. There are overall 120 operations of the point group Ih. ， hold a Megaminx in the Cartesian coordinate reference system. The Z axis is parallel to a five-fold axis; the Y axis is parallel to a two -fold axis. A Megaminx has 12 faces. According to symmetry， there are 10 C3 axes overall. There are two unique symmetry operations associated with a single C3 axis， the three corner cubies of the triangle still keep counterclockwise permutation . First。

there are overall 20 C3 symmetry operations.