Not sure if this really deserves a thread on its own, but I guess a mod can merge it into the squan discussion thread if not.
The left/right labelling of the paws and fists follows Jaap's square-1 page.
Peacock = cccccee (aka "pair")
Arrow = ccccece (aka "perpendicular")
Badge = cccecce (aka "parallel", "crown")
The numerical shape names should be self-explanatory (the number of edges between the corners, read clockwise, skip all zeros).
This table lists the average optimal slices to go from a random shape (weighted by frequency) to the specified shape. For the "exact" column, exactly that shape has to be the result (e.g. for the first row, 24/arrow doesn't count as the correct shape; rotating is not allowed), while the "equiv" column allows for all symmetrically equivalent shapes (e.g. for the first row, these are arrow/24, arrow/42, 24/arrow, 42/arrow).
(Is there a way to make the table not extend to the edges of the post? Could've sworn there was an option for that in the past.)
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Interesting to see that square-square (i.e. solving cubeshape as per normal) is actually the worst shape to aim for. (Which makes sense in hindsight, because it's only connected to kite-kite.)
Among the depth-3 cubeshape cases, scallop-kite has the lowest average distance (2.35 slices), opposite paws has the second lowest (2.43 slices), and everything else has 2.77 slices or more. This provides some justification for why scallop-kite is such a good beginner/intermediate-level method for solving cubeshape: it's Pareto-optimal between being easy to get into, and also being easy to get to cubeshape from.
Lining it up against the other Pareto-optimal cubeshape methods making use of an intermediate shape:
arrow-24 (1.85 slices to this, 5 more slices to cubeshape)
arrow-123 (2.03 slices to this, 4 more slices to cubeshape)
scallop-kite (2.35 slices to this, 3 more slices to cubeshape)
opposite fists (2.91 slices to this, 2 more slices to cubeshape)
square-square (4.62 slices to this, 0 more slices to cubeshape)
(There is no Pareto-optimal method that uses a depth-6 or depth-7 intermediate shape because those methods are uniformly worse than arrow/24. Using kite-kite as an intermediate shape is just solving cubeshape normally.)
The left/right labelling of the paws and fists follows Jaap's square-1 page.
Peacock = cccccee (aka "pair")
Arrow = ccccece (aka "perpendicular")
Badge = cccecce (aka "parallel", "crown")
The numerical shape names should be self-explanatory (the number of edges between the corners, read clockwise, skip all zeros).
This table lists the average optimal slices to go from a random shape (weighted by frequency) to the specified shape. For the "exact" column, exactly that shape has to be the result (e.g. for the first row, 24/arrow doesn't count as the correct shape; rotating is not allowed), while the "equiv" column allows for all symmetrically equivalent shapes (e.g. for the first row, these are arrow/24, arrow/42, 24/arrow, 42/arrow).
| shape | exact | equiv |
|---|---|---|
arrow/24 | 2.0310 | 1.8515 |
r.fist/scallop | 2.0962 | 1.8885 |
peacock/123 | 2.1077 | 1.9228 |
r.fist/shield | 2.2289 | 1.9516 |
arrow/123 | 2.2181 | 2.0288 |
arrow/15 | 2.1631 | 2.0305 |
peacock/15 | 2.1528 | 2.0321 |
peacock/114 | 2.0593 | 2.0332 |
badge/123 | 2.3061 | 2.0517 |
kite/l.paw | 2.3583 | 2.1060 |
l.fist/l.paw | 2.2811 | 2.1071 |
arrow/33 | 2.1354 | 2.1223 |
shield/l.paw | 2.3714 | 2.1321 |
barrel/l.paw | 2.4171 | 2.1756 |
r.fist/l.paw | 2.3464 | 2.2213 |
mushroom/r.fist | 2.5731 | 2.2273 |
badge/15 | 2.4812 | 2.2365 |
l.paw/scallop | 2.4002 | 2.2567 |
arrow/114 | 2.3138 | 2.3051 |
peacock/24 | 2.5068 | 2.3219 |
mushroom/l.paw | 2.5759 | 2.3322 |
kite/scallop | 2.3605 | 2.3475 |
r.fist/barrel | 2.6993 | 2.3491 |
peacock/33 | 2.3681 | 2.3583 |
arrow/6 | 2.3719 | 2.3654 |
badge/114 | 2.3888 | 2.3801 |
r.paw/l.paw | 2.4296 | 2.4252 |
l.paw/l.paw | 2.6357 | 2.4747 |
kite/shield | 2.5394 | 2.5329 |
badge/24 | 2.6656 | 2.5895 |
arrow/222 | 2.5965 | 2.5922 |
kite/r.fist | 2.9951 | 2.6580 |
square/scallop | 2.6911 | 2.6846 |
square/l.paw | 2.8874 | 2.7047 |
square/shield | 2.7765 | 2.7700 |
badge/6 | 2.7792 | 2.7760 |
kite/mushroom | 2.8233 | 2.8189 |
mushroom/scallop | 2.8548 | 2.8483 |
barrel/scallop | 2.8559 | 2.8494 |
mushroom/shield | 2.8668 | 2.8603 |
badge/33 | 2.8858 | 2.8825 |
r.fist/r.fist | 2.9685 | 2.8989 |
kite/barrel | 2.9092 | 2.9048 |
l.fist/r.fist | 2.9244 | 2.9146 |
peacock/6 | 2.9701 | 2.9603 |
square/r.fist | 3.2833 | 2.9625 |
barrel/shield | 2.9869 | 2.9804 |
square/mushroom | 2.9962 | 2.9918 |
scallop/scallop | 3.0033 | 3.0033 |
star/53 | 3.0147 | 3.0103 |
star/62 | 3.0174 | 3.0131 |
shield/scallop | 3.0381 | 3.0283 |
star/44 | 3.0587 | 3.0560 |
badge/222 | 3.0756 | 3.0734 |
shield/shield | 3.1294 | 3.1294 |
star/71 | 3.1697 | 3.1653 |
peacock/222 | 3.1854 | 3.1822 |
square/barrel | 3.2811 | 3.2768 |
mushroom/barrel | 3.2860 | 3.2817 |
star/8 | 3.2942 | 3.2898 |
kite/kite | 3.6264 | 3.6264 |
mushroom/mushroom | 3.7526 | 3.7526 |
barrel/barrel | 3.7531 | 3.7531 |
kite/square | 3.8923 | 3.8902 |
square/square | 4.6243 | 4.6243 |
(Is there a way to make the table not extend to the edges of the post? Could've sworn there was an option for that in the past.)
---
Interesting to see that square-square (i.e. solving cubeshape as per normal) is actually the worst shape to aim for. (Which makes sense in hindsight, because it's only connected to kite-kite.)
Among the depth-3 cubeshape cases, scallop-kite has the lowest average distance (2.35 slices), opposite paws has the second lowest (2.43 slices), and everything else has 2.77 slices or more. This provides some justification for why scallop-kite is such a good beginner/intermediate-level method for solving cubeshape: it's Pareto-optimal between being easy to get into, and also being easy to get to cubeshape from.
Lining it up against the other Pareto-optimal cubeshape methods making use of an intermediate shape:
arrow-24 (1.85 slices to this, 5 more slices to cubeshape)
arrow-123 (2.03 slices to this, 4 more slices to cubeshape)
scallop-kite (2.35 slices to this, 3 more slices to cubeshape)
opposite fists (2.91 slices to this, 2 more slices to cubeshape)
square-square (4.62 slices to this, 0 more slices to cubeshape)
(There is no Pareto-optimal method that uses a depth-6 or depth-7 intermediate shape because those methods are uniformly worse than arrow/24. Using kite-kite as an intermediate shape is just solving cubeshape normally.)
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