Table of Contents

1. Introduction
2. Starting the game
3. Movement
   1. Slide
   2. Pivot
   3. Nudge
4. Objective
   1. Goal
   2. Win Condition
5. Congratulations!
6. General Comments
7. Notation
8. Variations
9. Special Thanks

Introduction

This game is made possible by players like you.

There are two types of game pieces in Topoi: each player has an Onko ('Hunk' or 'Mass), as well as nine Lithoi (plural for Lithos, or 'Stone'), referred to as 'Stones'. The Prâgma (Objective) of the game is to completely surround your opponent's Onko (their single larger stone) with your own stones, your opponents stone., or the boundary of the board. There are three basic movements for the stones; Slide, Pivot, and Nudge.

Starting the game

The following diagrams are of two different recommended starting setups (one for beginners, and one for competitive play), followed by explanations and diagrams of the movements, then by diagrams of different examples of black completing their objective and a list of variations.

Movement

One of the beautiful and unique aspects of the game is that stones may move together if connected. Two or more stones are considered connected if they lay on consecutive adjacent nodes, in any formation. For example, a straight line, zig-zag, diamond, or hexagon. Stones that are not connected may not be moved together in the same turn. Onkos cannot connect or move with other Stones. A player has two options during their turn: relocate their Onko to an empty adjacent node. or move up to any number of connected stones in one of the following three ways:

1. Slide The most basic and intuitive of the stone movements, its power is not to be underestimated. The player picks a direction along which the stones will move. The Stones can move as far across the board as the player desires, as long as they are not obstructed by another piece of any color. The pieces that have slid must maintain their original formation. Each stone must slide the same number of nodes. Stones must be connected order to slide together. Note that individual stones can slide on their own.

   White Black Reset

   Diagram 2a: A 6-Stone slide-path shown for white. A 1-Stone slide-path shown for black. Note that there are many different options for each player.

2. Pivot The most difficult move to visualize, once mastered, provides potent leverage to a player's Stones. The player chooses a Stone (not an Onko) to act as an anchor, then chooses up to 3 Stones Connected to the anchor to 'Pivot' in either direction, up to five nodes, or 300° (the sixth being a full rotation, not a legal move). The Stones being pivoted must retain their original formation (the same angles between them) and must remain connected without going through any other pieces along any intermediate pivot path, or outside of the boundary of the board.

   Diagram 2b: Two different pivot paths for black shown. Four different pivot paths shown for White. Note that toward the bottom of the diagram, White's Pivot-Path-2 appears to Pivot through' or 'around' a black stone. This is a legal pivot because the Black Stone does not lay in an intermediate pivot path (White's Pivot-Path-1a). Asimilar situation is depicted toward the top of the diagram involving Black's Stones and White's Onko. Note that there are many diferent options for each player

3. Nudge Simple and elegant, is a useful tactic from early to late game. The player selects a Stone to Nudge to an adjacent free node. The player may then choose a Stone that was adjacent to that Stone and nudge to replace it. The effect is similar to that of a snake. A player chooses how many consecutive pieces to nudge. However, the pieces must be connected in a single string (they cannot nudge from two branches of a 'fork' in a single turn).

   Diagram 2c: Two Nudge-Paths shown for both Black and White. Note that there are many different options for each player

Objective

1. Goal The Prågma ('Object') of the game is to completely surround your opponent's Onko. When an Onko is one turn away from being surrounded, it is said to be in 'Kinó' (Move').

2. Win Conditions The following diagrams are examples of Black completing their objective.

   Diagram 3a Black completing their objective.

   Diagram 3a Black completing their objective.

   Note that any number of Black or White pieces may surround an Onko, the non-surounded player completing their objective.

Congratulations!

You are now equipped to play the game. Once the first person achieves their objective the game is over. Whoever had the most fun is the winner. Both players should agree upon the rules before the beginning of the game. isted below are a few general comments, and interesting variations, including an especialy interesting one that incorporates a new movement: The Swap

General Comments

There are a few edge cases that should be discussed.

1. Double Kinó The following Diagram depicts asituation where both player's Onkos are in Kinó.
   Diagram 4a Both players are in Kinó. If either player Slides a Stone to the specified node, both players will simultaneously complete their objective. If either player is to slide into place. The game is considered a draw.

Notation

Variations

The rules described above make for an exciting, dynamic game. Below are a few variations to consider. This list of variations is not exhaustive.

1. Special Movements, restrictions, and expansions The Four Basic Movements are dynamic, and comprise the spirit of the game. Any of them can be restricted or expanded. For example, the Pivot is well defined for any number of nodes Connected to an anchor, along the Pivot Paths described above, or along concentric hexagons with the anchor as the locus. Depending on on how the Pivot is defined, Pivot-Paths, and thus blocking, may be interpreted differenty. The Nudge could be expanded to as many nodes as are available (think Nudge and Slide comtbined). The Slide could be expanded to be able to change direction (think more than one Slide in one move). The Relocation could be restricted using the 'Away from the Center' mechanic described below under The Swap. Other Restrictions and Expansions of the Four Basic Movements are possible. The following Movements are considered Special, and should be agreed upon before the start of the game. They add additional elements, and can be played competitively if the players or organization so chooses. This list of Special Movements is not exhaustive. Each of them can be restricted or expanded in their own right, including combinations with the Four Basic Movements. (For example, a rule where Stone(s) can slide and swap with other Stone(s) in the same move).
   1. The Swap Aplayer may swap their Onko with an adjacent Stone of any color, toward the boundary, away from the center of the board. An Onko may only Swap With an adjacent stone laying in the immediate larger concentric hexagon. Swapping cannot take place along the boundary of the same hexagon. For example, an Onko positioned at (1,4,a) may only swap with an adjacent Stone positioned at (6,5,e), (1,5,a) or (1,5,b). An Onko positioned at (1,5,b) may only Swap with an adjacent Stone positioned at (1,6,b) or (1,6,c). In other words, An ONko may only swap with an adjacent Stone (of either color), if after it has done S0 its H coordinate has increased by 1. Note that if a player's Onko is on a line that extends from the center, it has three possible nodes to swap to. An OnKO in he center of the board has six possible nodes to swap to. Otherwise, they ony have two
   2. The Send A player may replace an adjacent Stone of any color, in any dìrection, with their Onko. That Stone is then placed into the owner's hand and the owner places it onto one of a selected number of nodes agreed upon beforehand (usualy the boundary). Play then proceeds as normal,the next turn being that of the player that did not just Send with their Onko. This can also be restricted using the "Away from the Center" mechanic described above in The Swap".
   3. The Burrow For either the Stones and/or Onkos (to be decided beforehand). A player may 'Burrow a piece while adjacent to (or occupying) one of a selected number of nodes agreed upon beforehand and 'Reemerge' onto one of a selected number of nodes agreed upon beforehand. The selected Stones may be marked and color-coded to create distinct 'Burrow' paths.
2. Removal Any player that sits to play the game may ask, "Is there a way of removing Stones from the game?" There are a few different variations that are playable and affect the game and win conditions in subtle ways. These Removal rules may also be restricted or expanded. This list is not exhaustive.
   1. Surrounding a Stone When a Stone is completely surrOunded by Stones of another color, the surrounding player may remove the Stone from the board. They could also 'Send' the Stone to one of a selected number of nodes agreed upon beforehand.
   2. Jumping' a Stone A player may ´Jump' an adjacent Stone of any color, in a straight line, with their Onko, away from the center of the board. The jumped Stone is removed from play, or sent to one of a selected number of nodes agreed upon beforehand.
3. Placement The rules listed above do not allow for placement of Stones. The game could be played with placement allowed onto one of a selected number of nodes agreed upon beforehand
4. Limitations and Handicapping Snegial Movements may be inventoried elegantly, by keeping Stones of different lers on the side of the board, and removing them as they are used (For example, each player may Swap or Send in any direction, but only once with nch color. keeping a Stone of each color on the side board in their inventory.) These tvpes of 'Limitations' can also be used to handicap a player (perhaps second to move, or the less skilled of the twO players), or to control game lenath Other methods of handicapping include:
   1. A player playing with extra Stones on the board
   2. A player choosing a number of opponents starting nodes
5. Alternative Win Conditions The win condition described above leads toa dynamic, enjoyable game. There are many other win conditions that could be chosen. A few options are listed below. This list is not exhaustive.
   1. A race of Onkos Building the largest contiguous cluster of Stones
   2. Creating the largest Bubble Onkos can Connect to Stones This variation is self explanatory, and can be restricted or expanded in a number of ways.
6. Game Board and Starting Setup While starting setup depicted above is well-balanced, and leads to interesting games between players of equal skill level, there is a plethora of options tor starting positions that lead to interesting games. The game can be played on boards of many diferent sizes, with different numbers of Stones (the mininmum depending on the win condition). Smaller boards typically lead to shorter games.

Special Thanks

Many thanks and much gratitude to:

Sheila Tilert - For loving me and offering me limitless patience and encouragement.

Ravi Hausner - For being welcoming, wary, and for humoring me endlessly.

Russ Allnutt - For being the best kind of friend anyone could ask for.

Vishnu Dorbala - For sharing my excitement, and being the first self-declared enthusiast.

Noah Chrein - For teaching me, leaming from me, and helping me to see things differently.

Joe Peckham - For always being ready to try something new.

The Wheaton High School Chess Club '23-24 - For inspiring me, and being my toughest critics.

As well as: Stephen Sorokanich, Liam Fowl, Paul Shackel, Barbara Little, Travis Williams, Jermain McDermott, Ankit Etha, Evan Flickinger, Estelle Keener, Eliana Murrell, Steven Little, Spiros Lentas, Ishfaaq Imtiyas,Jesse Millzman, and Luis Suarez.