-----------------------
SPIKE PATTERN

(F2 R2 Uv2)15   2 spike

(L2 R2 B2 Uv1)6 = 24 total moves

(F2 R2)3 (BR2 B2)3 (BL2 L2)3 = 18 moves

-----------------------
DOT PATTERNS

(U2 D2' F B' Uv)10
generates the 6 spot (centre 120 degree rotation of period 3, the first spot process)

(F2 U D' L2 Uv)4 U2' D2
improved 6 spot order 3

(F2 U D' L2 Uv2)4 
another improvement on 6 spot order 3, 16 moves

(U2 D2' F2 B2 Uv)4
generates the 6 spot (centre 120 degree rotation of period 3)

U2 D2' L2 BR2 U2 D2' F2 B2 U2 D2' R2 BL2 U2 D2' BR2 L2 (6 spot, face turn only, no rotations)

----------------------
H PATTERNS

L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 D' (32 moves)
6 H order 3

(D1 L2 R2 D2 L2 R2 D2 L2)2 (U' BR2 BL2 U2' BR2 BL2 U2' BR2)2  (6 H order 3, 32 moves)

(F2 R2 U1 D5 L2 F2)4 = 24 total moves (317.042 s)   6 H order 3 

F2 R2 (U D' L2 R2)3 U D' L2 F2 
6 H order 3, partially repeating, 18 moves

(U2 D' F2 B2)6    6 H order 2

----------------------
CROSS PATTERNS

D' L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 U2 D2'
6 cross order 3

L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 U2 D3
6 cross order 3 improved

(F2 R2 U1 D5 L2 F2)4  U2 D2'
6 cross order 3 (26 moves)

(F2 L2 U3 D3 R2 F2 L2)4 = 28 total moves (5480.8 s)
6 cross order 3, fully repeating

F2 R2 (U D' L2 R2)3 U D' L2 F2 U2 D2'
6 cross order 3, 20 moves

(F B' Uv)45 → 6 cross, 2 spike

(U1 D2 F2 B2 D3 F2 B2)3 = 21 total moves (138.468 s) 
6 cross order 2, fully repeating

-----------------------
Z PATTERNS

((D2' F2 U2 B2)3 Uv2')20   6 Z Order 3
((D2' F2 U2 B2)3 Uv2)4     6 Z order 3

-----------------------
X PATTERNS

L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 U2 D3 (Uv' B2 F2 D2 U2')4
6X order 3 (49 face turns)

(F2 R2 U1 D5 L2 F2)4  U2 D2' (B2 F2 D2 U2' Uv')4
6X order 3 (42 face turns)

(F2 R2 U1 D5 L2 R2 U1 D5 L2 R2 U1 D5 L2 R2 U1 D5 L2 F2) U2 D2' (B2 F2 D2 U2' Uv')4
6X order 3 (36 face turns)

(F2 R2 U1 D' L2 R2 U1 D' L2 R2 U1 D' L2 R2 U1 D' L2 ) B2 D2 U2' Uv' (B2 F2 D2 U2' Uv')2 B2 F2
6X order 3 (30 face turns)

(F2 R2 U1 D' (L2 R2 U1 D')3 L2) B2 D2 U2' Uv' (B2 F2 D2 U2' Uv') B2 F2 D2 U2' BR2 L2 
6X order 3 (30 face turns, restated)

(F2 B2 L2 BR2 R2 BL2 Uv)4   6 I pattern
(U2 D2 F2 B2 R2 L2 BR2 BL2 Uv2)20  6 I pattern

----------------------
DIAGONAL PATTERNS

L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 D' ((D2' F2 U2 B2)3 Uv2)4
6 diagonals order 3

((D2' F2 U2 B2)3 Uv2)4 (F2 R2 U1 D5 L2 F2)4
6 diagonals order 3

----------------------

CORNER TWISTS

(U1 L3 U2 F2 L1)6 = 30 total moves       (twist 9 corners)
(U4 L1 F1 L2 U4 F3 L2)4 = 28 total moves (twist 9 corners)
(U1 L1 U5 L3 U3 F2 U4 F2 L3)3 = 27 total moves (twist 9 corners)

(L F R)30 is equivalent to:
F L R2 F' L F2 L F' L R F' L F R2 F L F' R' F'   6 twist of corners < L, F, R> subgroup
U R U' R U' R2 U R U R' (U' R)2 U2 R' U' R'      2 twist of corners

----------------------
EDGE FLIPS

(U F R' F)30   6 flip
Flipped edges: 6 Edges flipped: [ "B-U", "BR-U", "F-U", "L-U", "BL-U", "F-D" ]

U R U F U' R' U' R F' R2 F2 R F' R' F' R   2 flip (works on cube as well)
Edges flipped: [ "F-R", "F-L" ]

U F U L U' F' U' F L' F2 L2 F L' F' L' F   2 flip
Edges flipped: [ "F-U", "L-U" ]

L' F2 L F L F' L2 F2 L F' U F U L' U' F' U' F L   2 flip (both edges in U face, U-L and U-F)

(U F3 U2' F2 U2 F L3 U' L)2    2 flip (result of repeating move search)

(U F U L U' F' U' F L' F2 L2 F L' F' L' F Uv2)3   flip all 6 middle edges

(L' U L U' L' U' F U2 L U' F' U' F L' F2 L F U Uv)6  12 flip of edges

F (L F L' U)7 F' Uv B' (BR' B' BR D')7 B Uv  16 flip of edges

F (L F L' U)7 F' Uv B' (BR' B' BR D')7 B Uv U R U F U' R' U' R F' R2 F2 R F' R' F' R
18 flip of edges, the superflip

(BR' B' BR D')7 (L' U L U' L' U' F U2 L U' F' U' F L' F2 L F U Uv)6 Uv4 L' U L U' L' U' F U2 L U' F' U' F L' F2 L F U
18 flip or superflip, 178 moves

F (L F L' U)7 F' Uv B' (BR' B' BR D')7 B Uv U R U F U' R' U' R F' R2 F2 R F' R' F' R
18 flip of edges, the superflip

L (BL L BL' U)7 L'  B' (BR' B' BR D')7 B U BR U R U' BR' U' BR R' BR2 R2 BR R' BR' R' BR
18 flip (78 unit turns)

((U1 D1 U5 R1 D5 R3 F3 R2)6 Uv2)3
18 flip (repeating solution, flip 6 edges 3 times)

((D1 R2 F1 D4 F2 R3 D1 F2)3 Uv2)3
18 flip (repeating solution, 72 moves)

(F U R)18  2 flip
(F' U' L')18  2 flip
U2 F' U' F' L F L' U F U2' F U F R' F' R U' F'   flips F-U R-U

I solved the 2 flip pattern in the U face myself. I adapted the 2 flip in the F face pattern:
L' F2 L F L F' L2 F2 L F' U F U L' U' F' U' F L  flips L-U F-U

U R U F U' R' U' R F' R2 F2 R F' R' F' R F U R U F U' R' U' R F' R2 F2 R F' R' F' R F'
4 flip all F face edges (34 moves)

(R2 U' R2 U1 F1 R1)4
4 flip all F face edges (24 moves)

R2 U' R2 U1 F1 R' U' R2 U1 F1 R' U' R2 U1 F1 R' U' R2 U1 F1 R1
4 flip all F face edges (21 moves)

(L F L' U)7  8 flip
(BR' B' BR D')7   8 flip

GAP solutions
-------------

L' U L U' L' U' F U2 L U' F' U' F L' F2 L F U2 L U2' F U F2 L F U' L' F' L F U F U L U' L' F' L2 F U' F' U L' F' L' F L' U L' U' L2 U L U' L' U' F U F' U' L' F' L F U L' U' F' L' F L U L'
80 moves for 2 flip pattern

L' U L U' L' U' F U2 L U' F' U' F L' F2 L F U
18 moves for different 2 flip (use a segment of the above solution)

----------------------
EDGE CYCLES

(D1 L2 R2 D2 L2 R2 D2 L2)2 = 16   two edge 3 cycles in D face

(U2 F2 L2 F2 U3 F2 L2 F2)4 = 32 total moves (127.68 s)  edge 3 cycle in U face
found by searching for repeating sequences

(R' D' R D2)18  edge 5 cycle
R D3 R2 D' R' D R2 D3 R' D2' R' D3 R2 D R' D' R2 D3 R D2

(R' D' R D' R' D R D' R' D2 R D)6  edge double swap in D
(L U L' U L U' L' U L U2' L' U')6 central reflection of above

(D3 F1 R1 D2 R3)6    edge double swap in D improvement (30 moves)
(D' R2 F2 D2' R2 D2 F2 R2)2   edge double swap in D (16 moves)

python3 solve-prism-edge2.py -g L,U,F "(L-U, F-U) (R-U, BR-U)"
L2 U2 F2 U' F2 L2 F2 L2 F2 L2 U F2 U2' L2  edge double swap in U
                                    
python3 solve-prism-edge2.py -g L,U,F "(L-U, F-U, R-U)"
L2 U L2 F2 L2 U L2 U' F2 L2 F2 U' F2 L2

python3 solve-prism-edge2.py -g L,U "(L-U, F-U, R-U, BR-U, B-U)"
U3 L U2' L2 U2' L2 U L U2' L U L2 U L' U4 L2 U2 L2 U3 L2 U4 L    edge five cycle 

L U F U' F' L' U F' L' U' L U F U'   edge three cycle L-U, F-U, R-U  14 moves, found by GAP

(U L U L' U L U2' L' U L U L' U L U2' L')3  improvement

Scramble (48 moves): U L U L' U L U2' L' U L U L' U L U2' L' U L U L' U L U2' L' U L U L' U L U2' L' U L U L' U L U2' L' U L U L' U L U2' L'
Double edge swap
Searching for optimal solution...
============================================================
✓ Solution found in 19 moves: L U2' L' U L U2' L U2 L' U2' L' U L' U2 L2 U2' L' U2 L2
============================================================
Time elapsed: 40.8771 seconds
States explored: 550,952
States/second: 13,478
✓ Solution verified correct!

Scramble (16 moves): U F U L U' F' U' F L' F2 L2 F L' F' L' F
2 flip
Searching for optimal solution...
============================================================
✓ Solution found in 16 moves: F' L F L F' L2 F2 L F' U F U L' U' F' U'
============================================================
Time elapsed: 168.6028 seconds
States explored: 2,032,946
States/second: 12,058
✓ Solution verified correct!

(L U L' U L U' L' U L U2' L' U')6 U' (L U L' U L U' L' U L U2' L' U')6 U   3 cycle of edges in U
U L2 U2 L2 U2 L2 U2 L2 U   3 cycle of edges in U

R F2 L' U' L' U2 L' (U' L)2 U L2' U L U' L2  F2 R'   3 cycle of edges in D
BL' B2 BR D BR D2' BR (D BR')2 D' BR2 D' BR' D BR2  B2 BL  3 cycle of edges in U

D3 L D L' D L' D' L2 D' L' D L' D L D   3 cycle of edges in D (L-D, F-D, R-D)

(L D L' D L D2' L' D)6   double edge swap order 2


Center of hexagonal prism group (6 elements):

    Identity (solved position) ✓
    Superflip (all 18 edges flipped) ✓
    Supertwist+ (all 12 corners twisted clockwise) ✓
    Supertwist- (all 12 corners twisted counterclockwise) ✓
    Superflip + Supertwist+ ✓
    Superflip + Supertwist- ✓


Your virtual prism is essentially a topological puzzle, not a geometric one.
That is, it’s implementing a consistent color permutation group, but not a physically embeddable 3D mechanism.

The top and bottom faces are regular hexagons subdivided into trapezoidal facelets — which works fine visually.
But when you give quarter turns to the lateral sides, you are assuming they behave as cubic strips, which geometrically would require:

    the side rectangles to rotate into each other on axes that bisect 120° angles — impossible for rigid shapes.

So yes — your remark that “trapezoids aren’t going to magically turn into rectangles” is precisely the reason the physical puzzle couldn’t exist, even though the math does.