This is the Icosoku. It is a new puzzle invented by a puzzle creator, Andrea Mainini. Our project studies the mathematical properties of the Icosoku and attempts to obtain a manual solution for the puzzle. We utilised many different methodologies to obtain results to solve our research questions and meet our objectives. Although we faced many limitations and difficulties, we were able to accomplish our initial objectives, which was to analyse the mathematical properties of the puzzle, analyse the existing algorithm and come up with a manual solution for the puzzle. Scroll down and click on the links to find out more about the different methods we used!
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Notations and Terminologies
There are certain terminologies that we have come up with and will be using in our following pages. In order to avoid confusion, here is the list of terminologies that we will be using:
Icosahedron
A platonic solid that has 12 vertices and 20 triangular faces, each vertex surrounded by 5 faces. This is the shape of the original puzzle.
Octahedron
A platonic solid that has 6 vertices and 8 faces, each vertex surrounded by 4 faces.
Tetrahedron
A platonic solid that has 4 vertices and 4 faces, each vertex surrounded by 3 faces.
Pin
This refers to the yellow pins provided as part of the puzzle. They are to be placed into the puzzle in order to set-up the puzzle for solving. Placing these pins into the puzzle is analogous to the shuffling of a Rubik’s Cube.
Configuration
This refers to the position the yellow pins are placed into the puzzle. Note that configurations are the same if they can be obtained through a rotation of the puzzle.
Tile
This refers to the white triangular tiles provided as part of the puzzle. They are to be placed into triangular spaces on the Icosoku frame. If placed in the right order, the puzzle will be in the solved state.
Solved state
This refers to the state in which the number of dots, on the vertices of the tiles surrounding a pin, is equal to the number on the pin for all pins.
Icosahedron
A platonic solid that has 12 vertices and 20 triangular faces, each vertex surrounded by 5 faces. This is the shape of the original puzzle.
Octahedron
A platonic solid that has 6 vertices and 8 faces, each vertex surrounded by 4 faces.
Tetrahedron
A platonic solid that has 4 vertices and 4 faces, each vertex surrounded by 3 faces.
Pin
This refers to the yellow pins provided as part of the puzzle. They are to be placed into the puzzle in order to set-up the puzzle for solving. Placing these pins into the puzzle is analogous to the shuffling of a Rubik’s Cube.
Configuration
This refers to the position the yellow pins are placed into the puzzle. Note that configurations are the same if they can be obtained through a rotation of the puzzle.
Tile
This refers to the white triangular tiles provided as part of the puzzle. They are to be placed into triangular spaces on the Icosoku frame. If placed in the right order, the puzzle will be in the solved state.
Solved state
This refers to the state in which the number of dots, on the vertices of the tiles surrounding a pin, is equal to the number on the pin for all pins.
MethodologyWe tried many different ways to come up with a solution for the puzzle and investigated its properties. Click to learn more.
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ResultsAfter proceeding with our methodology, we yielded results, of course. Some were successful, others not so much. Click to learn more.
ExtensionsThere is more that could be done besides what we have already attempted. How can this research be extended? Click to learn more.
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ConclusionWhat do our results mean? What can we derive from our results? Click to learn more.
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