Metatron's Dilemma: Culturally Relevant STEAM Game Design

Metatron The ArchAngel has lost the source of his power from a cube that contains five three-dimensional objects—tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedrons—that are the basis for everything in the physical world and as a blueprint from which all life springs. These objects are dispersed in artist John Biggers’, "The Quilting Party," overseen by three forces: family and the morning and evening stars (see below). They can also be found in M.C. Escher's "Stars."

Each three-dimensional figure has an equal side length, equal face size, and equal angle. Moreover, these figures fit perfectly within a sphere. These figures are regarded as the building blocks of the universe and they are equated with five elements: fire, earth, air, water, and ether.

The goal of this project is to design and build a physical board game that uses knowledge of geometry principles (i.e., in Sacred Geometry), natural elements, and shows how these principles / elements in art can help players win the game.

The game board and pieces can be created using cardboard, Inkscape; or modeled in Tinkercad and exported for 3D printing.

• Cardboard or Tinkercad 3D Design (for creating the game pieces)
• Cutting tools (for cardboard)
• Inkscape or another vector graphics software to design the game board, or
• Markers and rulers to draw the game board
• Poster board, a large format printer, or laser cutter
• 3D Printer for 3D game pieces

"The Quilting Party," an early 1980s mural by the late artist John Biggers inspires the Metatron's Dilemma board game. The mural imparts layered meanings as recognizable symbols of daily life in the American south and spiritual connections to African heritage (article is included as a PDF). Mathematics often appears in the mural with pyramids, musical instruments, five regular polyhedra (Platonic solids), and fractal geometry. The game extracts aspects of the artwork and translates it for the game.

Another artwork titled "Stars" by M.C. Escher also uses similar geometric figures and principles. Like Biggers, Escher was interested exploring math as well as the laws of the physical nature of the universe, or Sacred Geometry. You can read more about Sacred Geometry here:https://medium.com/@TheConstructionZone/what-s-so-... Find out more about both artists below:

As an inquiry-based activity, ask students to look closely at one of these artworks (or choose your own) and make a list of what geometric figures they can identify. Also, ask students to think about why the artist used the figures and what the artwork means. Their answers can be used to create challenge cards for the game. Later, you will need to print out or project the artwork as a reference during game play.

Metatron's Cube contains all the geometric shapes and patterns that exist, from the spirals of snail shells to the hexagonal shapes of a honeycomb. There are similar geometric codes in flowers, snowflakes, DNA molecules, organic life forms and heavenly bodies. Within the Cube are five Platonic Solids and the natural elements each represents:

• Star Tetrahedron - Fire
• Hexahedron - Earth
• Octahedron - Air
• Icosahedron - Water
• Dodecahedron - Ether

The game board design is based on Metatron's Cube. A copy of the diagram is included.

For this step, students can manually draw the diagram on poster board or print it out using a large format printer (file is included). If you have access to a laser cutter you can etch the design in cardboard or wood.

Another option is to create a new vector-based design for the game board using Inkscape and print it out.

A manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it. For this step, students will use Tinkercad 3D Design to create geometric manipulatives based on the Platonic Solids. Players will be able to use these objects to answer questions. The list includes:

• Star Tetrahedron (see images and below)
• Hexahedron(can be found in Tinkercad > Basic Shapes)
• Icosahedron (can be found in Tinkercad > Basic Shapes)
• Octahedron
• Dodecahedron

In Tinkercad > Basic Shapes you will find the Hexahedron (cube) and Icosahedron but the other shapes need to be created using the online software. The Star Tetrahedron is made up of two Tetrahedra. Import one tetrahedron (included), then copy or duplicate it. Turn the second one upside down 180 degrees and combine the two shapes. (see images)

Students will need to figure out how to use the Tetrahedron or other 3D shapes to create the remaining objects.

Students can also use cardboard to create the 3D objects (see image). Create the 2D patterns (for cutting) using templates from this website: https://www.templatemaker.nl/en/platonic-solids.

For this step, students will design 3D pieces that can be used to play the game such as:

• Die/dice (to get a number for how many steps to move)
• 5 Tokens (to represent natural elements such as fire, water)
• 6 Pawns (to move to different positions on the board)

Steps for how to build a pawn using Tinkercad 3D Design is provided (see images):

1. Open Tinkercad
2. Click the "Create New Design" button
3. Drag two or three Basic Shapes to the Workplane (ex. sphere, paraboloid, cylinder)
4. Combine the shapes to create a pawn
5. Explore as an STL file for 3D printing

Steps to create a token using Inkscape and Tinkercad includes (see images):

1. Find and save a black and white graphic (clipart) for each element
2. Open the graphic file using Inkscape
3. "Vectorize" the graphic using the Trace Bitmap option
4. Save as an SVG file
5. Import SVG file into Tinkercad and use it to create the token
6. Repeat previous steps for each element
7. Explore as an STL file for 3D printing

Students can also use found objects or build their game pieces using markers and cardboard.

To unlock the mystery of Metatron’s Cube, players must answer a series of questions based on five elements and five symbols that are embedded in John BIggers's mural and represented as physical objects (Platonic Solids) on the game board. Players must answer the questions correctly to win the game.

For this step, create 3-6 cards for each Platonic Solid and include one for the artwork (see image).

Metatron's Dilemma consists of one die, six home bases, center base, and six pawns (colors are up to you). Up to six players can play this game. To play, each player

1. Starts by setting a pawn at home base (choose a circle)
2. Roll the die to get a number; whoever has the highest number can go first
3. Roll a second time to move to a circle
4. In order to advance, players must pick a card and correctly answer the question. Once answered correctly, the player gets a token.
5. Players must move counter-clockwise using the black circles. It doesn't matter which circle they land in, as long as it's not occupied by another pawn (or they lose a turn and must return to center or home base).
6. The first player to collect all five tokens wins the game.

For this step, have students create their own sets of rules for game play.

Finally, test out the game and have students take turns playing it.