Twin puzzles that look the same but behave differently

[Renslay]

I love the fact that the FTO (face-turning octahedron) and the CTO (corner-turning octahedron) looks exactly the same, yet they are completely different puzzles. FTO is quite unique in many ways, while CTO is just an edge-only super 3x3 variant. (See first image: FTO and CTO slightly turned)

I had a similar experience when I ordered a Senso Circle 4x4 v2. I thought it is the same as the Crazy 4x4 v2. They look exactly the same, but there is a slight difference: when making a wide turn, one inner circle stays, but the other turns! In the case of the Crazy 4x4, the inner circles always turn (see second image). This slight difference makes them completely different puzzles, with different properties. For example, in the case of the Crazy 4x4, "adjacent" center-wings stay together, forming a virtual single piece. In Senso, it is the opposite center-wings who stay together! I also find the Senso much, much harder to solve.

I'm wondering, what other puzzle-siblings or puzzle-families are out there. In the case of the FTO-CTO, the cut is different, yet they look the same. It makes me wonder, is there a "megaminx" that turns/cuts across the red line (third image)?

What other "twin puzzles" exist that look the same but behave very differently?

 

[Chicken-Cuber]

Wait what’s the last one

 

[qwr]

HKnowstore has many of these. My favorites are the latch cube, which is a clever modification of a standard 3x3 to achieve the locking effect

And the 3x3 mixup cube, which looks like a standard 3x3 with weird proportions until you see the insane 45 deg move

 

[stoic]

Cool thread. You've touched on "crazy" puzzles with the crazy 4x4s so the multiple series Dayan "planets" spring to mind. Crazy pentahedrons, crazy megaminxes and crazy 3x3x3s (eight of each per "family"). All look the same but have different numbers of "0" and "1" faces.

As for your deep-cut minx idea, I'm not aware of a commercially-available version but the chopasaurus has been demonstrated. (Also, video here.)

Oh, and I thought of another one - starminx I and II (corner turning and face turning).

 

[Renslay]

HKnowstore has many of these. My favorites are the latch cube, which is a clever modification of a standard 3x3 to achieve the locking effect

And the 3x3 mixup cube, which looks like a standard 3x3 with weird proportions until you see the insane 45 deg move

Ah, the latch cube and the mixup cube! I have both, love them.

I wouldn't count the latch cube here: technically any puzzle can be turned into a latch variant, so from the perspective of looking for twins, it's not that interesting (even if the puzzle itself is interesting and quite challenging!)

The mixup cube is more intriguing! The only nitpick is that the middle layer have to be 1.41 times wider than the outer layer, a small visual discrepancy. But it is surely confusing when you show it to others who haven't seen it before.

Cool thread. You've touched on "crazy" puzzles with the crazy 4x4s so the multiple series Dayan "planets" spring to mind. Crazy pentahedrons, crazy megaminxes and crazy 3x3x3s (eight of each per "family"). All look the same but have different numbers of "0" and "1" faces.

As for your deep-cut minx idea, I'm not aware of a commercially-available version but the chopasaurus has been demonstrated. (Also, video here.)

Oh, and I thought of another one - starminx I and II (corner turning and face turning).

Oooh, that chopasaurus looks amazing! And exactly what I had in mind. I knew something like that must exist.

Starminx 1 and 2 are another perfect example for such twins! Somehow I imagine that the corner turning variant is much easier than the deep cut version...

 

[Lucas Garron]

FTO and VTO are total classics! They're really fun to show people in person.

 Twizzle link 

2BL' BR' 2BL' 2L 2BL BR 2BL' 2L' 2BL'

 Twizzle link 

2U_R_BR_BB' 2U_L_F_R 2U_R_BR_BB 2U_L_F_R2' 2U_BB_BL_L 2U_L_F_R 2U_BB_BL_L'

 

[Puzzle Maniac]

FTO and VTO are total classics! They're really fun to show people in person.

 Twizzle link 

2BL' BR' 2BL' 2L 2BL BR 2BL' 2L' 2BL'

 Twizzle link 

2U_R_BR_BB' 2U_L_F_R 2U_R_BR_BB 2U_L_F_R2' 2U_BB_BL_L 2U_L_F_R 2U_BB_BL_L'

What does the V in VTO stand for?

 

[Renslay]

What does the V in VTO stand for?

My guess is vertex. Or a typo.

 

[Jacck]

I'm wondering, what other puzzle-siblings or puzzle-families are out there. In the case of the FTO-CTO, the cut is different, yet they look the same. It makes me wonder, is there a "megaminx" that turns/cuts across the red line (third image)?

View attachment 39250

At least you can "create" it with twizzle (no idea whether you could built a real one):

 Twizzle link 

URBR

 

[stoic]

Starminx 1 and 2 are another perfect example for such twins! Somehow I imagine that the corner turning variant is much easier than the deep cut version...

Yes, I have the corner turning one and IIRC it's solvable using only simple swaps.

 

[Renslay]

FTO and VTO are total classics! They're really fun to show people in person.

 Twizzle link 

2BL' BR' 2BL' 2L 2BL BR 2BL' 2L' 2BL'

 Twizzle link 

2U_R_BR_BB' 2U_L_F_R 2U_R_BR_BB 2U_L_F_R2' 2U_BB_BL_L 2U_L_F_R 2U_BB_BL_L'

Yes, these look so cool!
My favorite trick is an algorithm that twists 2 corners on the FTO...
Then doing the same by literally twisting 2 corners on the CTO

 

[Puzzle Maniac]

My guess is vertex. Or a typo.

Yes, I was also figuring it was a typo of CTO.

 

[Lucas Garron]

My guess is vertex.

This. The `cubing.js` code base tends to use "vertex" when referring to polyhedra. Both are fine, of course.

"CTO" also has another very common meaning in tech, so I tend to avoid it as a puzzle name.