HyperDimension Chess
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HDC Handbook

Special Rules

Last updated: June 1, 2026

HDC still includes castling, en passant, and promotion. These rules remain familiar, but they are adapted to three-dimensional space.

This page explains the three special rules clearly enough that you can recognize them in play.

Remember

Special moves are also made only on the 2D board. If a special move is legal, the app marks the relevant target squares there.

Castling

HDC has two forms of castling:

  • horizontal castling like in classical chess
  • vertical Z-castling along the layers

Shared conditions

For every castling move:

  • the king and the involved rook must never have moved
  • the king must not start in check
  • the squares between them must be empty
  • the king must not enter or cross an attacked square
  • castling is one move: king and rook move together

Horizontal castling

This happens on layer IV.

Short

Notation: O-O

White example:

  • king: E1–IV → G1–IV
  • rook: H1–IV → F1–IV

Long

Notation: O-O-O

White example:

  • king: E1–IV → C1–IV
  • rook: A1–IV → D1–IV

Black castles accordingly on rank 8.

Vertical Z-castling

This is the HDC-specific castling move along file E.

Lower Z-castle

Notation: O-Oz

White example:

  • king: E1–IV → E1–II
  • rook: E1–I → E1–III

Upper Z-castle

Notation: O-O-Oz

White example:

  • king: E1–IV → E1–VI
  • rook: E1–VIII → E1–V

The same safety rules apply as in horizontal castling.

Z-castling in HDC with king and rook moving along file E through multiple layers
Horizontal castling stays familiar for chess players. The diagram therefore focuses on HDC-specific Z-castling: king and rook move along the layers on file E.

En passant

In HDC, en passant still works only on the immediately following move after the opposing pawn’s double-step.

Core idea

The capturing pawn moves to the skipped intermediate square.

What is new in HDC

Because pawns can also capture diagonally with a layer change, en passant in HDC is not limited to the same layer.

In principle there are:

  • the classical XY version
  • an additional YZ version involving layers

Notation

Add: e.p.

Examples:

  • exd6–IV e.p.
  • e5–Vxe6–IV e.p.
En passant in HDC with double-step, skipped intermediate square, and layer relation
As in classical chess, the key square is the one skipped by the double-step. What is new in HDC is that the capturing pawn may also reach that square through a layer relation.

Promotion

A pawn is promoted as soon as it reaches the final enemy rank.

  • White at Y = 8
  • Black at Y = 1

This applies on every layer.

Promotion choices

  • Queen
  • Duke
  • Rook
  • Bishop
  • Knight

No promotion to a king.

Notation

Add =Piece, for example:

  • e8–II=Q
  • ...=D

Why special rules matter so much in HDC

Castling

It is not only protection, but also spatial repositioning.

En passant

It shows that pawn logic remains precise even inside the 3D system.

Promotion

It can happen on every layer and can create powerful new piece choices, including the Duke.

Common mistakes

  • forgetting Z-castling
  • trying en passant too late
  • overlooking attacked transit squares in castling
  • expecting promotion only on layer IV
  • forgetting the Duke as a promotion option

Mini FAQ

Does HDC really have two castling directions?

Yes. A horizontal one on layer IV and a vertical one along the Z-axis.

Can en passant involve a layer change?

Yes, in principle through the YZ capture logic of pawns.

On which layers can promotion happen?

On all layers. The deciding factor is the reached rank, not the layer.

Can I promote to a Duke?

Yes.

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