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docs/puzzles/2x2x2x2.md

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# 2x2x2x2
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!!! info inline end "2x2x2x2"
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![2x2x2x2 in HSC](/assets/images/HSC2222.png)
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![2x2x2x2 in Hyperspeedcube](https://cloud.hypercubing.xyz/assets/img/virt/hsc_2x2x2x2.png)
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**Shape:** Tesseract
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## Physical version
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![physical 2x2x2x2](/assets/images/2_4_transparent.png){width="20%"}
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![physical 2x2x2x2](https://cloud.hypercubing.xyz/assets/img/phys/melinda_2x2x2x2_render.png){width="20%"}
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Since 2013, Melinda Green has been refining her [physical 2x2x2x2](/puzzles/physical/2x2x2x2). See her [project home page](https://superliminal.com/cube/2x2x2x2/) for more details.
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docs/puzzles/3x3x3x3.md

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# 3x3x3x3
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!!! info inline end "3x3x3x3"
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![3x3x3x3 in HSC](/assets/images/3_4_transparent.png)
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![3x3x3x3 in Magic Cube 4D](https://cloud.hypercubing.xyz/assets/img/virt/mc4d_3x3x3x3.jpeg)
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**Shape:** Tesseract
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## Turning
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Each turn of the 3^4^ is a rotation of one of its cubic cells (which can be oriented in any of 24 orientations of a cube). A normal move disturbs 8 4c, 12 3c, and 4 2c pieces.
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Each turn of the 3^4^ is a rotation of one of its cubic cells (which can be oriented in any of 24 orientations of a cube). A normal move disturbs 8 4c, 12 3c, and 4 2c pieces.
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## History
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docs/puzzles/physical/1x2x2x2.md

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# Tymon's 1x2x2x2
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!!! info inline end "Tymon's 1x2x2x2"
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![Tymon's 1x2x2x2](https://cloud.hypercubing.xyz/assets/img/phys/tymofro/1x2x2x2.jpeg)
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![Tymon's 1x2x2x2](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x2x2x2.jpeg)
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**4D Shape:** Hypercuboid
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Legal moves of a layer include basic 2x2x2 90° twists, 180° twists in any plane which also rotate pieces in 4d axis, or a combination of both.
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![Tymon's 1x2x2x2 with one half exposed](https://cloud.hypercubing.xyz/assets/img/phys/tymofro/1x2x2x2_split.jpeg){width="50%"}
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![Tymon's 1x2x2x2 with one half exposed](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x2x2x2_split.jpeg){width="50%"}
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## Solving
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docs/puzzles/physical/1x2x2x3.md

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# Tymon's 1x2x2x3
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!!! info inline end "Tymon's 1x2x2x3"
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![Tymon's 1x2x2x3](https://cloud.hypercubing.xyz/assets/img/phys/tymofro/1x2x2x3.jpeg)
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![Tymon's 1x2x2x3](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x2x2x3.jpeg)
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**4D Shape:** Hypercuboid
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Legal moves of a layer include basic 2x2x2 90° and 180° twists that rotate pieces without changing their 4d orientation, 4d 180° twists that besides moving pieces in 3d, rotate them in 4d axis, or a combination of both.
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![Tymon's 1x2x2x3 with one half exposed](/assets/images/3221phys_1.jpeg){width="50%"}
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![Tymon's 1x2x2x3 with one half exposed](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x2x2x3_split.jpeg){width="50%"}
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## Solving
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docs/puzzles/physical/1x2x3x3.md

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# Tymon's 1x2x3x3
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!!! info inline end "Tymon's 1x2x3x3"
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![Tymon's 1x2x3x3](/assets/images/3321phys.jpeg)
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![Tymon's 1x2x3x3](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x2x3x3.jpeg)
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**4D Shape:** Hypercuboid
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docs/puzzles/physical/1x3x3x3.md

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# Tymon's 1x3x3x3
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!!! info inline end "Tymon's 1x3x3x3"
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![Tymon's 1x3x3x3](/assets/images/3331phys.jpeg)
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![Tymon's 1x3x3x3](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x3x3x3.jpeg)
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**4D Shape:** Hypercuboid
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Legal moves of a layer include 90° twists, 180° twists in any plane, or a combination of both.
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![Tymon's 1x3x3x3 with one half exposed](/assets/images/3331phys_1.jpeg){width="50%"}
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![Tymon's 1x3x3x3 with one half exposed](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x3x3x3_split.jpeg){width="50%"}
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## Solving
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This puzzle has two 1c pieces that are physicaly represented by one 2c piece (the core). Technically the puzzle is solved only when all of the other pieces have the pink sticker on the outside cell (because pink is outside on the core piece). To be able to solve the puzzle with purple color facing outwards, Tymon created a gyro algorithm that flips all pieces inside out and puts the core outside of the puzzle. This represents that pink/purple axis is flipped and now the puzzle is only solved when all of the pieces are oriented with purple on the ouside. The gyro can be reversed to get back to default projection.
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![1x3x3x3 gyro gif](/assets/images/3331gyro.gif){width="50%"}
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![1x3x3x3 gyro gif](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x3x3x3_split.gif){width="50%"}
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### OLL Parity
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The original solved state well represents which sticker on a piece is on the inside and which one is on the outside, but some people prefer a solved state with edges rotated 4 dimensionaly. This is because then the overall look of the puzzle is less chaotic and more friendly to non hypercubers.
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![Tymon's 1x3x3x3 alternative solve state](/assets/images/3331physalt.jpeg){width="50%"}
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![Tymon's 1x3x3x3 alternative solve state](https://cloud.hypercubing.xyz/assets/img/phys/tymon_1x3x3x3_alt.jpeg){width="50%"}

docs/puzzles/physical/2x2x2x2/index.md

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# Melinda's 2x2x2x2
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!!! info inline end "Melinda's 2x2x2x2"
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![Melinda's 2x2x2x2](/assets/images/2_4_transparent.png)
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![Melinda's 2x2x2x2](https://cloud.hypercubing.xyz/assets/img/phys/melinda_2x2x2x2_render.png)
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**4D Shape:** Tesseract
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### Invention
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Many hypercubers, including [Melinda Green](https://superliminal.com/) (one of the developers of MC4D) wanted to create a physical 3^4^, but sadly it just seemed too complicated. Eventually, she decided to focus on the 2^4^ due to its simplicity of only having 16 4c pieces.
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Throughout 2013 and 2014, Melinda was in contact with [Oskar van Deventer](https://oskarvandeventer.nl/), and together they tried to think of any possible mechanism for a physical 2^4^. Originally they were determined to find a good mechanism that didn't have to rely on magnets, but after several failed attempts a magnetic mechanism was the only solution. In 2017, Melinda built the first prototype and shared an unlisted [YouTube video](https://www.youtube.com/watch?v=Asx653BGDWA) showing it off to the mailing list members.
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Throughout 2013 and 2014, Melinda was in contact with [Oskar van Deventer](https://oskarvandeventer.nl/), and together they tried to think of any possible mechanism for a physical 2^4^. Originally they were determined to find a good mechanism that didn't have to rely on magnets, but after several failed attempts a magnetic mechanism was the only solution. In 2017, Melinda built the first prototype and shared an unlisted [YouTube video](https://www.youtube.com/watch?v=Asx653BGDWA) showing it off to the mailing list members.
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A few months later, Melinda built a 2nd prototype using 3D printing from a company called Shapeways (which just so happened to offer 8 colors, 6 of them being standard Rubik’s Cube colors, plus pink and purple (this is where the standard 4D colour scheme comes from)).
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### Popularization
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!!! tip inline "Professor Erno Rubik inspecting a physical 2^4^ at G4G 2018"
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![Erno Rubik inspecting Melinda's 2x2x2x2](/assets/images/ErnoInspects2222.jpg)
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![Erno Rubik inspecting Melinda's 2x2x2x2](https://cloud.hypercubing.xyz/assets/img/phys/melinda_2x2x2x2_erno_inspects.jpeg)
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At the Gathering For Gardner conference of 2018, Roice Nelson got to show his physical 2^4^ to Erno Rubik. It was reported that his only comment was something along the lines of “none of the derivative puzzles matter and that only his original invention is important”.
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!!! example "Animations showing how the virtual and physical 2^4^ transform into each other"
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<center>
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![physical to virtual 2x2x2x2 transformation 1](/assets/images/2222Phys_Virt.gif){width="40%"}
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![physical to virtual 2x2x2x2 transformatio 2](/assets/images/wip_physical_virtual_24_animation_v2.gif){width="40%"}
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![Physical to virtual 2x2x2x2 transformation 1](https://cloud.hypercubing.xyz/assets/img/phys/melinda_2x2x2x2_anim1.jpeg){width="40%"}
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![Physical to virtual 2x2x2x2 transformation 2](https://cloud.hypercubing.xyz/assets/img/phys/melinda_2x2x2x2_anim2.jpeg){width="40%"}
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Each twist and rotation on the virtual 2^4^ is possible to do on the physical puzzle, albeit with certain moves requiring some extra setup. See the [canonical moves](/puzzles/physical/2x2x2x2/canonical-moves) page for a more detailed explanation.

docs/puzzles/physical/2x2x2x3.md

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# Grant's 2x2x2x3
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!!! info inline end "Grant's 2x2x2x3"
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![Grant's 2x2x2x3](/assets/images/grantsPhys2223.png)
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![Grant's 2x2x2x3](https://cloud.hypercubing.xyz/assets/img/phys/grant_2x2x2x3_render.png)
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**4D Shape:** Hypercuboid
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In December of 2021, Melinda green posted this image to the Hypercubers Discord server, jokingly calling it a 2x2x2x3:
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![Melinda's 2x2x2x3](/assets/images/melinda2223.jpg){width="40%"}
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![Melinda's 2x2x2x3](https://cloud.hypercubing.xyz/assets/img/phys/melinda_2x2x2x3.jpeg){width="40%"}
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After Melinda posted that, Luna started sketching out some ideas of possible layouts for an actual 2x2x2x3.
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<img src="/assets/images/3c.png" alt="Physical 3C piece rendering" width="150" align="right">
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<img src="https://cloud.hypercubing.xyz/assets/img/phys/3c.png" alt="Physical 3C piece rendering" width="150" align="right">
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She invented the design for the 3c pieces by dividing the edges of a cube into 12 sections like this, grouping 4 sets of 3 together symmetrically.
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This is when Grant joined the server, and shared his 3D printed 2x2x2x2. Rowan then challenged him to build Luna's design for the 2x2x2x3. After a lot of time tweaking the designs, printing them, magnetizing them, and assembling them, the 2x2x2x3 was completed on February 3rd 2022.
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![Grant's physical 2x2x2x3 shortly after finishing assembly](/assets/images/phys2x2x2x3finished.jpg){width="200"}
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![Grant's physical 2x2x2x3 shortly after finishing assembly](https://cloud.hypercubing.xyz/assets/img/phys/grant_2x2x2x3.jpeg){width="200"}
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## How Does it Work?
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docs/puzzles/physical/2x2x3x3.md

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# Grant's 2x2x3x3
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!!! info inline end "Grant's 2x2x3x3"
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![Grant's 2x3x2x3](/assets/images/grant2233render_noline.png)
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![Grant's 2x2x3x3](https://cloud.hypercubing.xyz/assets/img/phys/grant_2x2x3x3_render.png)
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**4D Shape:** Hypercuboid
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After the invention of grant's 2x2x2x3, hypercubers were already thinking about what was next. The 2x2x3x3 has an extra middle layer that the 2x2x2x3 doesn't have, which introduces the 2c piece to the design. Hactar designed the new 2c piece, and then Grant made the first rendering of what a physical 2x2x3x3 would look like.
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![Grant's 2x3x2x3](/assets/images/grant2233render_noline.png){width="50%"}
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![Grant's 2x2x3x3](https://cloud.hypercubing.xyz/assets/img/phys/grant_2x2x3x3_render.jpeg){width="50%"}
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It took a while to get the designs just right, but after printing and assembling 4 of the new 2c pieces and 8 more 3c pieces, the puzzle was completed on May 14th, 2022.
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It took a while to get the designs just right, but after printing and assembling 4 of the new 2c pieces and 8 more 3c pieces, the puzzle was completed on May 14th, 2022.
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## Functionality
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In order to prove that it was fully functional, it had to be shown that moves matched the virtual puzzle, and that it was possible to gyro the puzzle into different orientations.
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In order to prove that it was fully functional, it had to be shown that moves matched the virtual puzzle, and that it was possible to gyro the puzzle into different orientations.
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The gyro starts by removing the middle layer, and then gyroing just like the 2x2x2x3, which involves separating that middle layer and then gyroing like a 2x2x2x2. Next, the middle layer has some 4 dimensional black magic done to it, and then finally the puzzle is reassembled into the gyroed state. After doing this, Grant realized that some of the 2x2x3 cell moves aren’t accessible, meaning that we actually need a 2nd type of gyro! This secondary gyro involves centering a 2x2x3 cell, and then making the middle layer stick out. Now the puzzle was fully functional.

docs/puzzles/physical/2x3x3x3.md

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# Grant's 2x3x3x3
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!!! info inline end "Grant's 2x3x3x3"
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![Grant's 2x3x3x3](/assets/images/2333.png)
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![Grant's 2x3x3x3](https://cloud.hypercubing.xyz/assets/img/phys/grant_2x3x3x3_render.png)
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**4D Shape:** Hypercuboid
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docs/puzzles/physical/3x3x3x3.md

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# Grant's 3x3x3x3
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![physical 3x3x3x3](/assets/images/physical3333.png){width="100%"}
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![physical 3x3x3x3](https://cloud.hypercubing.xyz/assets/img/phys/grant_3x3x3x3_render.png){width="100%"}
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**4D Shape:** Tesseract
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At first, it was not clear how to expand the physical 2x3x3x3 into the 3x3x3x3, as it would need extra pieces that would no longer make it a nice cuboid shape. This is because we have one more slice layer than the number of dimensions we're trying to simulate. For example a 3x3x3 has 3 slice layers, so to represent it in 2D space, some of the pieces have to stick out like this:
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![2D exploded view of the 3x3x3](/assets/images/2Dexploded3x3x3.png)
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![2D exploded view of the 3x3x3](https://cloud.hypercubing.xyz/assets/img/phys/grant_3x3x3.png)
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After months and months of effort, Grant completed assembling the puzzle on July 22nd, 2022. To this day, Grant has not scrambled or solved the physical 3x3x3x3 due to it being extremely big, heavy, and awkward to use. The most that was done on it was a checkerboard algorithm, but he did make a video showing off all of the [hypercuboids and their legal twists](https://www.youtube.com/watch?v=geFPbJAfLF4).
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![Grant holding the physical 3x3x3x3](/assets/images/grant_phys3333.jpg){width="70%"}
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![Grant holding the physical 3x3x3x3](https://cloud.hypercubing.xyz/assets/img/phys/grant_3x3x3x3.jpg){width="70%"}
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In April 2023, Akkei made a new program that simulated the physical 3^4^, and then Hyperespy became the first person to ever fully solve the physical 3^4^. The actual gyros are pretty painful to do, but luckily the program does them for you :)
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