# An Intro to Diagonal and Orthogonal Movement on Exotic Grids

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

**This is a Octagon Tessellation, square and octagon grid, 8&4 Grid, or 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 Grid**A Rook on a 9 Grid

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