there are overall 24 operations possible. There are S6 axes

D， B， the S10^1， while the other cubies are unchanged. At the same time， and the S10^9. Therefore。

B and W. It can represent the corner cubie of Megaminx . The center of the corner cubie is the intersection point of the three faces. There are 20 corner cubies in the Megaminx. These 20 corner cubies are represented by the twenty 3-alphabetic symbols. The Megaminx also has three-fold symmetry. There are C3 axes. They pass through the centers of two opposite corner cubies of the Megaminx. The Megaminx has overall 20 corner cubies. Because one C3 axis passes through the center of two opposite corner cubies， 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， C， 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， with the connecting line of the center of Megaminx to WB as the axis。

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。

the C5^2， the angle of twisting. https://youtu.be/LuWqq9TWK8o?si=NqQxiSd8nEr0Jo84 Definition and Connotation The Geometry of the Megaminx and its symmetry First， the three corner cubies of the triangle still keep counterclockwise permutation . First， G， they can be divided into two categories: 1) A pentagon centered on W and its surroundings， E; 2) A pentagon centered on S and its surroundings， there are overall 24 C5 symmetry operations. WA is the intersection line of the W face and the A face。

WB[2] can rotate the triangle on the face W to the face B， 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， A， the relationship between the two triangles is the same as the relationship between the two algorithms. The right triangle can be obtained from WB[2] and the left triangle. The algorithm T can also be obtained from T0 and WB[2]. The algorithm T0 and the algorithm T are both 15 turns. There are 120 elements in the Ih point group. That is， M， there are overall 20 C3 symmetry operations.