square is to triangle as cube is to

square is to triangle as cube is to

Have you ever thought about this question “square is to triangle as cube is to” Today on Solsarin we’re going to answer this question.

square is to triangle as cube is to
square is to triangle as cube is to

What is the triangle cube?

The Pyraminx, also known as the triangle Rubik’s Cube is a tetrahedron-shaped 3-layered twisty puzzle
having four triangular faces which are all divided into nine identical smaller triangles.
This is the second best selling puzzle toy in the World after the Rubik’s Cube with over 100 million pieces sold.

It was invented by Uwe Mèffert (Germany) in 1971 but it was patented only later seeing the success of the Rubik’s Cube in 1981.
Meffert invented several other famous puzzles like the Megaminx, Skewb, Skewb Diamond, Teraminx, Dogic (icosahedron-shaped puzzle), and the list goes on.
Other inventors were inspired by the 4-axle mechanism, Tony Fisher used it for the Golden Cube and Golden Egg.

The first official WCA Pyraminx competition was organized in 2003 and the winner was the American Andy Bellenir who solved the puzzle in 14.09 seconds.
These days the best results range from 1 to 3 seconds, but the World record is under one second.

The Pyraminx family

The first puzzle on the image is not a 2×2 Pyraminx because that would be too simple where you would only have to turn the peaks and that would solve it instantly. The Pyramorphix is actually a 2×2 shape mod.
The third one is a Master Pyraminx, the 4×4 version of the puzzle.
It might be hard to believe that the Skewb is a Pyraminx shape mod. If you take apart the two puzzles you can see that they’re both built on a similar core mechanism.

Read More:

How to solve a Pyraminx

Solving a Pyraminx is much easier than a Rubik’s Cube. It has 3,732,480 possible permutations which is relatively a small number (similar to the 2x2x2 Pocket Cube)
so a personal computer can easily go through all of the possible scrambles. It can be solved from any random position in less than 12 moves.
I’m presenting below the easiest solution where you only have to learn a couple algorithms.

1. Notation

square is to triangle as cube is to
square is to triangle as cube is to

Let’s mark the four corners of the puzzle with letters, just like in the notation of the Rubik’s Cube
a letter by itself means a clockwise 120o turn of the corner and an apostrophe marks a counterclockwise turn (eg. R’).
We are going to use these letters to describe algorithms in this tutorial. For example: L’ F L F’

We can easily notice that there are three types of pieces: Corner tips (A), centers having one sticker each (B) and edges with two stickers (C).

2. Solving the tips and centers

square is to triangle as cube is to
square is to triangle as cube is to

The solution of the Pyraminx begins with turning the 4 corners (A) to match the center pieces.
this is just a simple turn for each corner because the three sides of the center pieces (B) are linked together.
When the tips are OK, deep turn the puzzle to make the three center colors match on all faces. Try to reach the state on the image above!
When you’re done all that’s left is solving the remaining 6 edge pieces (C).

3. Two edges next to one corner

square is to triangle as cube is to
square is to triangle as cube is to

In this stage we want to solve three edges around the top corner. Use the Right and Left algorithms below depending on the direction of the insertion.
These leave the pieces marked with the asterisk (*) in place. Usually you’ll need an algorithm for the last piece because the first two can be solved intuitively.

Right algorithm: R F R’ F’
Left algorithm: L’ F’ L F

4. Last layer edges

All that’s left is to permute/cycle the last layer edges.
Take the puzzle in your hands with the scrambled face on the left and perform the requred turns, depending on your case.

square is to triangle as cube is to
square is to triangle as cube is to

Clockwise cycle: U’ F U F’
Counterclockwise cycle: U L’ U’ L
Flip tow edges: F U’ F’ U F’ L F L’

Rubik’s Cube

The Rubik’s Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.
Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer.
Rubik’s Cube won the 1980 German Game of the Year special award for Best Puzzle.
As of January 2009, 350 million cubes had been sold worldwide, making it the world’s bestselling puzzle game and bestselling toy.

On the original classic Rubik’s Cube, each of the six faces was covered by nine stickers, each of one of six solid colours:
white, red, blue, orange, green, and yellow.
Some later versions of the cube have been updated to use coloured plastic panels instead, which prevents peeling and fading.
In models as of 1988, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white, and blue are arranged in that order in a clockwise arrangement.
On early cubes, the position of the colours varied from cube to cube. An internal pivot mechanism enables each face to turn independently, thus mixing up the colours.
For the puzzle to be solved, each face must be returned to have only one colour.
Similar puzzles have now been produced with various numbers of sides, dimensions, and stickers, not all of them by Rubik.

Although the Rubik’s Cube reached its height of mainstream popularity in the 1980s, it is still widely known and used.
Many speedcubers continue to practice it and similar puzzles; they also compete for the fastest times in various categories.
Since 2003, the World Cube Association, the international governing body of the Rubik’s Cube, has organised competitions worldwide and recognises world records.

Algorithms

In Rubik’s cubers’ parlance, a memorised sequence of moves that has a desired effect on the cube is called an algorithm.
This terminology is derived from the mathematical use of algorithm, meaning a list of well-defined instructions for performing a task from a given initial state
through well-defined successive states, to a desired end-state. Each method of solving the Cube employs its own set of algorithms
together with descriptions of what effect the algorithm has, and when it can be used to bring the cube closer to being solved.

Many algorithms are designed to transform only a small part of the cube without interfering with other parts that have already been solved
so that they can be applied repeatedly to different parts of the cube until the whole is solved.
For example, there are well-known algorithms for cycling three corners without changing the rest of the puzzle or flipping the orientation of a pair of edges while leaving the others intact.

Some algorithms do have a certain desired effect on the cube (for example, swapping two corners) but may also have the side-effect of changing other parts of the cube (such as permuting some edges).
Such algorithms are often simpler than the ones without side-effects and are employed early on in the solution when most of the puzzle has not yet been solved and the side-effects are not important.
Most are long and difficult to memorise. Towards the end of the solution, the more specific (and usually more complicated) algorithms are used instead.

Patent history

Nichols assigned his patent to his employer Moleculon Research Corp., which sued Ideal in 1982. In 1984, Ideal lost the patent infringement suit and appealed.
In 1986, the appeals court affirmed the judgment that Rubik’s 2×2×2 Pocket Cube infringed Nichols’s patent, but overturned the judgment on Rubik’s 3×3×3 Cube.

Even while Rubik’s patent application was being processed, Terutoshi Ishigi, a self-taught engineer and ironworks owner near Tokyo
filed for a Japanese patent for a nearly identical mechanism, which was granted in 1976 (Japanese patent publication JP55-008192).
Until 1999, when an amended Japanese patent law was enforced, Japan’s patent office granted Japanese patents for non-disclosed technology within Japan without requiring worldwide novelty.
Hence, Ishigi’s patent is generally accepted as an independent reinvention at that time. Rubik applied for more patents in 1980
including another Hungarian patent on 28 October. In the United States, Rubik was granted U.S. Patent 4,378,116 on 29 March 1983, for the Cube. This patent expired in 2000.

Trademarks

Rubik’s Brand Ltd. also holds the registered trademarks for the word “Rubik” and “Rubik’s” and for the 2D and 3D visualisations of the puzzle.
The trademarks have been upheld by a ruling of the General Court of the European Union on 25 November 2014 in a successful defence against a German toy manufacturer seeking to invalidate them.
However, European toy manufacturers are allowed to create differently shaped puzzles that have a similar rotating or twisting functionality of component parts such as for example Skewb, Pyraminx or Impossiball.

On 10 November 2016, Rubik’s Cube lost a ten-year battle over a key trademark issue. The European Union’s highest court, the Court of Justice
ruled that the puzzle’s shape was not sufficient to grant it trademark protection.

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