Pyraminx simulator and solver

Info

Pieces

Type	Count	Stickers	Positions	Orientation (physical)	Orientation (visual)
1	4	3	4	3	3
2	4	3	4	3	3
2	6	2	6	2	2

One row per orbit. Orientation counts are per position; multiple values mean positions differ.

Stickers

Axes

48 cut planes across them

Solver

Available

Distinct-piece states

≈ 7.56 × 10⁷906,992,640 arrangements of the stickers the moves reach (Schreier–Sims)÷ 12 turns of the whole puzzle= 75,582,720Tracks individual sticker identities, even on identical-looking pieces; whole-puzzle rotations are identified. Invisible rotations of a piece and internal pieces are not counted.

Visually distinct states

Not computedVisually distinct states = distinct-piece states ÷ reachable indistinguishable arrangements.Reachable indistinguishable arrangements = 1 × reachable fraction.No visually interchangeable sticker-bearing pieces were found.The reachable fraction accounts for restrictions such as permutation parity. Computing the correct fraction and the final visual state count is not yet implemented.

Put together at random

1 in 192 reaches the original sticker identities4!·3⁴ · 4!·3⁴ · 6!·2⁶ = 174,142,586,880 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 906,992,640 arrangements the moves reach = 192This uses distinct piece identities; the chance of reaching a visually solved state may be higher.

Moves

Vertex turns

Pyraminx beginner method

Align the centers and tips, build one layer, then solve the last three edges.

The detected first-layer face is below in the reference hold. Uppercase letters turn a vertex and its tip; lowercase letters turn only a tip. Whole-puzzle regrips are shown as preparation.

Align the centers

Align the four larger vertex pieces so their three colors agree with the puzzle's color arrangement.

Start with the larger pieces beneath the tips; ignore the edges for now.
Turn each vertex until its stickers face the matching sides. The reference frame follows the positions of these four pieces.

U turn

Turn the vertex until the three center stickers match the reference color arrangement. Edges can move during this stage.

Match the tips

Match each small tip to the aligned vertex beneath it.

Use lowercase moves to turn only a tip.
Match all three stickers of the tip to the neighboring center stickers.

Before this phase: Align the centers.

u turn

Turn only the small tip to match the center piece directly beneath it.

First-layer edges

Place the three edges around the bottom face, matching both colors of each edge.

Keep the bottom color below and find its matching edges.
Use a left or right insertion. Extract an edge from a wrong slot before reinserting it.
The grouped setup and undo keep the centers and tips aligned and restore edges already placed.

Before this phase: Align the centers, Match the tips.

Insert a first-layer edge from the right

[R, U]

Bring a first-layer edge into the front slot, insert it, and restore the upper vertex. Reverse the insertion to extract a misplaced edge. Centers and tips return to alignment.

Insert a first-layer edge from the left

[L', U']

Bring a first-layer edge into the front slot, insert it, and restore the upper vertex. Reverse the insertion to extract a misplaced edge. Centers and tips return to alignment.

Last three edges

Cycle or flip the final three edges to finish the Pyraminx.

Check both the position and orientation of the remaining edges.
Use the suggested cycle or two-edge flip. Some cases need a combination of these short algorithms.

Before this phase: Align the centers, Match the tips, First-layer edges.

Last-layer edge cycle

(R U' R') U' (R U' R')

Use the suggested hold and cycle or flip the last three edges. The first layer, centers, and tips stay solved.

Last-layer reverse edge cycle

(R U R') U (R U R')

Use the suggested hold and cycle or flip the last three edges. The first layer, centers, and tips stay solved.

Two-edge flip

R' L R L' U L' U' L

Use the suggested hold and cycle or flip the last three edges. The first layer, centers, and tips stay solved.

Well known algorithms and patterns

Beginner

Edge insertion — right

R U' R'

Edge insertion — left

L' U L

Last-layer edge cycle

(R U' R') U' (R U' R')

Last-layer reverse edge cycle

(R U R') U (R U R')

Two-edge flip

R' L R L' U L' U' L

Patterns

Superflip

(U R L')3

Derived pattern, verified to flip all six edges in place while preserving tips and centers.

Four twisted tips

u l r b

Turn each tip once; the rest of the puzzle stays solved.

Four twisted tips — inverse

(u l r b)'

Inverse of Four twisted tips; the rest of the puzzle stays solved.