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An Intro to Diagonal and Orthogonal Movement on Exotic Grids

May 8, 2012

After a lot of research and development, I’ve worked out orthogonal and diagonal movement for 7 different type of grids. I am not a mathematician, so my findings are very debatable. Essentially, I’m approaching this from a game theory mind set, because I am very interested in exotic grids being used in board games. These are my general findings without explanation. Each set of grids will receive their own post and explanation.

Part 1: Squares Hexagons and Triangles

Part 2: Coming Soon

Part 3: Coming Soon

Part 4: Coming Soon

This is a Grid. A Checkerboard, etc.

Orthogonal is how Rooks move.

Diagonal is how Bishops move.

This is a Hexgrid

A Rook on a Hex Grid

A Bishop on a Hex Grid

This is a Triangle Grid


A Rook on a Triangle Grid

A Bishop on a Triangle Grid

This is Pentagon Tessellation, pentagonal grid, pent grid, etc

A Rook on a Pent Grid

A Bishop on a Pent Grid

This is a Octagon Tessellation, square and octagon grid, 8&4 Grid, or Octo Grid

A Rook on a Octo Grid

A Bishop on an Octo Grid

Furthermore, Bishop on a Square,

This is a Septagon Grid, or 7 Grid

A Rook on a 7 Grid

Furthermore a Rook on an Hour Glass

A Bishop on a 7 Grid

A Bishop on an Hourglass

This is a Nonogon Tessellation, Starburst Grid, or 9 GridA Rook on a 9 Grid

A Bishop on a 9Grid

Bishop on a Starburst


A Decagon Tessellation, 10-8 Grid, or simply 10 Grid

A Rook on a 10 Grid

A bishop on a 10 grid

Bishop on the Hour Glass Space

Some Interesting Notes:

-Orthogonal and Diagonal Movement have two properties that can be ranked: direction and  number of edges used in a single move.

-Different Shapes provide different movement options

-Different orientations of the same shape, equally rotate the movement options

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