BrainPlay Wiki
Euclidean Dance
Euclidean Dance - Image3
Posting Details
Country of origin United States
Created by Matthew Renner
Posted by Matthew Renner
Date first posted February 10, 2014
Game details
Game genre Critical thinking
Game summary Each player has blocks that they rotate or mirror. When they rotate a block next to an opposing player’s blocks, they claim those blocks and add them to their own. A player wins when they capture every other player’s blocks.
# of players 2 to 3
For ages 6 to 12

Other details

Game Designer / Creator[]

  • Created by Matthew Renner

Game Summary[]

Euclidean Dance is a two or three player strategy game. Each player has blocks that they rotate or mirror. When they rotate a block next to an opposing player’s blocks, they claim those blocks and add them to their own. A player wins when they capture every other player’s blocks.

The game focuses on several cognitive functions. Players will mentally transform their game pieces and plan several moves in advanced. This game is fast-paced and can change momentum instantly; it will challenge players to develop new strategies while monitoring other players actions. The game can be played casually with friends or setup into a tournament.

Players / Moderators[]

  • Ages 6-12. 2-3 players.

Game Set-up and Construction[]


  • Game board.
    • 15x15 grid.
  • Game blocks.
    • Game blocks are a simple cube. Opposing sides of each cube is colored red, green, and blue.
    • Units are a set of adjacent blocks.
    • Players choose from five starting unit configurations. See Figure 1 for starting unit configurations.

Game Mechanics:

  • Movement (See Figure 2)
    • Adjacent blocks, or units, must move as one.
    • Units can be rotated ±90 and 180 degrees
  • Axis of rotations can be any vertex of any block within that unit (interior or exterior).
    • Units can be mirrored/flipped horizontally or vertically
  • Axis of the mirror can be any edge on the unit (interior or exterior).
    • Units can “pass through” other blocks during rotations, but the resting position of the unit cannot overlap any player’s blocks.
    • If a player has more than one block unit on the board, they may only move one of them for their turn.
  • Attacking (See Figure 3)
    • After a unit moves, any blocks which are adjacent to it are now “captured” and now belong to that player and that unit. Flip these blocks to the appropriate color.
  • Win Conditions
    • Capture all of your opponents’ blocks.

Game Workflow:

  • Choose game order.
    • For 2 player games, a coin is flipped.
    • For 3 player games, a block is rolled. The first color rolled starts, the second color rolled goes second, and the color not rolled goes last.
  • Players choose a starting unit configuration (See Figure 1)
    • Player may place the unit anywhere on the game board, but not adjacent to another players unit. Place these in the game order.
    • For 3 player games, each player gets two units; place the second set of units after the first round of unit placement.
  • Using the game order, players take turns moving and attacking, stating whether they are rotating or mirroring, and which axis they plan to use. See Figure 4 for example game play.

Alternative Game Play:

  • Create dead blocks and place them on the game board. Players may not land on these spaces.
  • Create “colorless” blocks and place them on the game board. These will not belong to a player until a player lands adjacent to it and captures it. This may require additional blocks to be made.

Templates / Diagrams[]

Euclidean Dance - Image1

Figure 1. Five initial block unit configurations: Players choose one of these units to start the game.

Euclidean Dance - Image2

Figure 2. Axis of rotation and mirroring for a typical unit: The left illustration shows in green which points around which the unit may rotate. The right illustration shows in green along which lines the player may flip the unit.

Euclidean Dance - Image3

Figure 3. Attacking mechanics: Player red rotates about the green axis. This moves their unit adjacent to three of blue’s blocks, highlighted in red dashes. Those three blocks are added to red’s unit. It is now blue’s turn.

Euclidean Dance - Image4

Figure 4. Example game play between two players: Each illustration shows that player’s intended move. The next frame shows the completed move and the opposing player’s intended move.

Euclidean Dance - Image5

Figure 5. Template of the game board.

Euclidean Dance - Image6

Figure 6. Template of the blocks: Make sure the block template and the game board template are printed at the same scale. For 2 player games, only 8 blocks are required, for 3 player games, 24 blocks are required.

Related Web Links[]

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Other Details[]

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