diff --git a/src/core/selection.ts b/src/core/selection.ts
index 44efcd0d..3bbe69c5 100644
--- a/src/core/selection.ts
+++ b/src/core/selection.ts
@@ -3,3 +3,28 @@ export type EditorSelection =
   | { kind: "brushes"; ids: string[] }
   | { kind: "entities"; ids: string[] }
   | { kind: "modelInstances"; ids: string[] };
+
+export function cloneEditorSelection(selection: EditorSelection): EditorSelection {
+  if (selection.kind === "none") {
+    return {
+      kind: "none"
+    };
+  }
+
+  return {
+    kind: selection.kind,
+    ids: [...selection.ids]
+  };
+}
+
+export function getSingleSelectedBrushId(selection: EditorSelection): string | null {
+  if (selection.kind !== "brushes" || selection.ids.length !== 1) {
+    return null;
+  }
+
+  return selection.ids[0];
+}
+
+export function isBrushSelected(selection: EditorSelection, brushId: string): boolean {
+  return selection.kind === "brushes" && selection.ids.includes(brushId);
+}
diff --git a/src/document/brushes.ts b/src/document/brushes.ts
new file mode 100644
index 00000000..2728232a
--- /dev/null
+++ b/src/document/brushes.ts
@@ -0,0 +1,117 @@
+import { createOpaqueId } from "../core/ids";
+import type { Vec3 } from "../core/vector";
+
+export const BOX_FACE_IDS = ["posX", "negX", "posY", "negY", "posZ", "negZ"] as const;
+
+export type BoxFaceId = (typeof BOX_FACE_IDS)[number];
+
+export interface BrushFace {
+  materialId: string | null;
+}
+
+export type BoxBrushFaces = Record<BoxFaceId, BrushFace>;
+
+export interface BoxBrush {
+  id: string;
+  kind: "box";
+  center: Vec3;
+  size: Vec3;
+  faces: BoxBrushFaces;
+  layerId?: string;
+  groupId?: string;
+}
+
+export type Brush = BoxBrush;
+
+export const DEFAULT_BOX_BRUSH_CENTER: Vec3 = {
+  x: 0,
+  y: 1,
+  z: 0
+};
+
+export const DEFAULT_BOX_BRUSH_SIZE: Vec3 = {
+  x: 2,
+  y: 2,
+  z: 2
+};
+
+function cloneVec3(vector: Vec3): Vec3 {
+  return {
+    x: vector.x,
+    y: vector.y,
+    z: vector.z
+  };
+}
+
+function cloneBrushFace(face: BrushFace): BrushFace {
+  return {
+    materialId: face.materialId
+  };
+}
+
+export function isBoxFaceId(value: unknown): value is BoxFaceId {
+  return typeof value === "string" && BOX_FACE_IDS.some((faceId) => faceId === value);
+}
+
+export function hasPositiveBoxSize(size: Vec3): boolean {
+  return size.x > 0 && size.y > 0 && size.z > 0;
+}
+
+export function cloneBoxBrushFaces(faces: BoxBrushFaces): BoxBrushFaces {
+  return {
+    posX: cloneBrushFace(faces.posX),
+    negX: cloneBrushFace(faces.negX),
+    posY: cloneBrushFace(faces.posY),
+    negY: cloneBrushFace(faces.negY),
+    posZ: cloneBrushFace(faces.posZ),
+    negZ: cloneBrushFace(faces.negZ)
+  };
+}
+
+export function createDefaultBoxBrushFaces(): BoxBrushFaces {
+  return {
+    posX: {
+      materialId: null
+    },
+    negX: {
+      materialId: null
+    },
+    posY: {
+      materialId: null
+    },
+    negY: {
+      materialId: null
+    },
+    posZ: {
+      materialId: null
+    },
+    negZ: {
+      materialId: null
+    }
+  };
+}
+
+export function createBoxBrush(
+  overrides: Partial<Pick<BoxBrush, "id" | "center" | "size" | "faces" | "layerId" | "groupId">> = {}
+): BoxBrush {
+  const center = cloneVec3(overrides.center ?? DEFAULT_BOX_BRUSH_CENTER);
+  const size = cloneVec3(overrides.size ?? DEFAULT_BOX_BRUSH_SIZE);
+
+  if (!hasPositiveBoxSize(size)) {
+    throw new Error("Box brush size must remain positive on every axis.");
+  }
+
+  return {
+    id: overrides.id ?? createOpaqueId("brush"),
+    kind: "box",
+    center,
+    size,
+    faces: overrides.faces === undefined ? createDefaultBoxBrushFaces() : cloneBoxBrushFaces(overrides.faces),
+    layerId: overrides.layerId,
+    groupId: overrides.groupId
+  };
+}
+
+export function cloneBoxBrush(brush: BoxBrush): BoxBrush {
+  return createBoxBrush(brush);
+}
diff --git a/src/geometry/box-brush.ts b/src/geometry/box-brush.ts
new file mode 100644
index 00000000..dd56415d
--- /dev/null
+++ b/src/geometry/box-brush.ts
@@ -0,0 +1,47 @@
+import type { Vec3 } from "../core/vector";
+import type { BoxBrush } from "../document/brushes";
+
+export interface BoxBrushBounds {
+  min: Vec3;
+  max: Vec3;
+}
+
+export function getBoxBrushHalfSize(brush: BoxBrush): Vec3 {
+  return {
+    x: brush.size.x * 0.5,
+    y: brush.size.y * 0.5,
+    z: brush.size.z * 0.5
+  };
+}
+
+export function getBoxBrushBounds(brush: BoxBrush): BoxBrushBounds {
+  const halfSize = getBoxBrushHalfSize(brush);
+
+  return {
+    min: {
+      x: brush.center.x - halfSize.x,
+      y: brush.center.y - halfSize.y,
+      z: brush.center.z - halfSize.z
+    },
+    max: {
+      x: brush.center.x + halfSize.x,
+      y: brush.center.y + halfSize.y,
+      z: brush.center.z + halfSize.z
+    }
+  };
+}
+
+export function getBoxBrushCornerPositions(brush: BoxBrush): Vec3[] {
+  const bounds = getBoxBrushBounds(brush);
+
+  return [
+    { x: bounds.min.x, y: bounds.min.y, z: bounds.min.z },
+    { x: bounds.max.x, y: bounds.min.y, z: bounds.min.z },
+    { x: bounds.min.x, y: bounds.max.y, z: bounds.min.z },
+    { x: bounds.max.x, y: bounds.max.y, z: bounds.min.z },
+    { x: bounds.min.x, y: bounds.min.y, z: bounds.max.z },
+    { x: bounds.max.x, y: bounds.min.y, z: bounds.max.z },
+    { x: bounds.min.x, y: bounds.max.y, z: bounds.max.z },
+    { x: bounds.max.x, y: bounds.max.y, z: bounds.max.z }
+  ];
+}
diff --git a/src/geometry/grid-snapping.ts b/src/geometry/grid-snapping.ts
new file mode 100644
index 00000000..737098d5
--- /dev/null
+++ b/src/geometry/grid-snapping.ts
@@ -0,0 +1,48 @@
+import type { Vec3 } from "../core/vector";
+
+export const DEFAULT_GRID_SIZE = 1;
+
+function assertGridSize(gridSize: number): number {
+  if (!Number.isFinite(gridSize) || gridSize <= 0) {
+    throw new Error("Grid size must be a positive finite number.");
+  }
+
+  return gridSize;
+}
+
+export function snapValueToGrid(value: number, gridSize = DEFAULT_GRID_SIZE): number {
+  const step = assertGridSize(gridSize);
+
+  if (!Number.isFinite(value)) {
+    throw new Error("Grid-snapped values must be finite numbers.");
+  }
+
+  return Math.round(value / step) * step;
+}
+
+function snapPositiveSizeValue(value: number, gridSize: number): number {
+  if (!Number.isFinite(value)) {
+    throw new Error("Box brush size values must be finite numbers.");
+  }
+
+  const snappedSize = Math.round(Math.abs(value) / gridSize) * gridSize;
+  return snappedSize > 0 ? snappedSize : gridSize;
+}
+
+export function snapVec3ToGrid(vector: Vec3, gridSize = DEFAULT_GRID_SIZE): Vec3 {
+  return {
+    x: snapValueToGrid(vector.x, gridSize),
+    y: snapValueToGrid(vector.y, gridSize),
+    z: snapValueToGrid(vector.z, gridSize)
+  };
+}
+
+export function snapPositiveSizeToGrid(size: Vec3, gridSize = DEFAULT_GRID_SIZE): Vec3 {
+  const step = assertGridSize(gridSize);
+
+  return {
+    x: snapPositiveSizeValue(size.x, step),
+    y: snapPositiveSizeValue(size.y, step),
+    z: snapPositiveSizeValue(size.z, step)
+  };
+}