Puzzle: Tetrahedron, Vertex Cut, Type B, 5th Order
Abbreviation: Tetra VB5
Commonly Known As: Professor Pyraminx

Piece Counts

Name	Qty	Colors	Orient.	Perm.	Orbits
Tip	4	3	3, Trivial	None	None
Corner	4	3	3	None	None
Inner Edge	6	2	2, Fixed	Even	None
Middle Edge	12	2	None	Even	None
Outer Edge	12	2	None	Even	None
Outer Face	12	1	None	Even	None
Inner Face	4	1	None	Even	None

Move Types

Type	Layer	Period	Pieces Affected	Total Parity
Vertex	1	3	1 tip twist	None
Vertex	2	3	1 corner twist, 1 outer edge 3-cyc	Even
Vertex	3	3	1 outer face 3-cyc, 1 inner edge 3-cyc, 1 middle edge 3-cyc	Even
Vertex	4	3	1 inner face 3-cyc, 2 outer face 3-cyc, 1 middle edge 3-cyc, 1 outer edge 3-cyc	Even

Suggested Solving Orders

Edge Reduction Cage Method
1. Group middle and inner edges
2. Group outer edges with middle/inner edge groups
3. Solve edges and tips
4. Solve inner faces
5. Solve outer faces

Important Issues and Notes
The three-cycle given for step 5 can be used to cycle two pieces within the same face, or three piece from all different faces by using U- then U+, etc.

Useful Algorithms
In step 1, three cycle middle edges: U[4]+ F[234]- U+ L- U[4]-
In step 2, three cycle outer edges: U[2]+ F[234]- U+ L- U[2]-
In step 3, three cycle edges: F[234]+ U+ F- U-
In step 4, three cycle inner faces: (R[23]+ U+ R- U+ R+ U+ R-) (R[4]+ U[2]- R[4]- U[2]- R[4]+ U[2]- R[4]-) U[34]+
In step 4, swap two pairs of centers: (R[234]+ L- R- L+) F+ (L- R+  L+ R-) F-
In step 5, three cycle outer faces: (R[4]+ U+ R-) U[3]+ (R[4]+ U- R-) U[3]-