# Cube

## Description

The Cube projection is a faceted projection consisting of six square sides, one for each pole and four along the equator centered at 135° and 45° west, 45° and 135° east meridians. It can be folded into a cube. Areas between 45° north and 45° south are projected with the plate carrée projection.

The Cube projection is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.0 and later.

## Projection properties

The subsections below describe the Cube projection properties.

### Graticule

Cube is a faceted projection. The meridians and parallels are equally spaced straight lines within 45° north and 45° south forming a grid of perfect squares. The polar facets project parallels as concentric squares centered on the pole, which is a point. The meridians are equally spaced straight lines originating in the center. The outline of the polar facet is a square of 45° parallel. At the junction of the equatorial facets with the polar facets, the meridians bend toward the pole. With certain polar facets' arrangements, the graticule can be symmetric across the equator and/or the central meridian.

### Distortion

The Cube projection is neither conformal nor equal-area. Shapes, areas, distances, directions, angles are all generally distorted. Between 45° north and 45° south, distortion properties follow the plate carrée projection. Shape, scale, and area distortion increase with the distance from the equator. North, south, east, and west directions are always accurate, but general directions are distorted, except locally along the equator. On the polar facets, directions are correct from the center. The scale is correct at the equator.

## Usage

The Cube projection is not recommended for general mapping.

## Limitations

The Cube projection is supported on spheres only. For an ellipsoid, the semimajor axis is used for the radius. Some equidistant and direction properties are not maintained when an ellipsoid is used.

## Parameters

Cube parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Option, used to display different arrangements of the polar facets with values as follows in the table below. The examples use the default central meridian value of 0°.
Option valuesDescriptionExample

0, 1, 2, or 3

The North Pole facet is aligned to the meridian that is 135° west of the central meridian.

The South Pole facet is aligned at 135° west, 45° west, 45° east, or 135° east, respectively, from the central meridian.

4, 5, 6, or 7

The North Pole facet is aligned to the meridian that is 45° west of the central meridian.

The South Pole facet is aligned at 135° west, 45° west, 45° east, or 135° east, respectively, from the central meridian.

8, 9, 10, or 11

The North Pole facet is aligned to the meridian that is 45° east of the central meridian.

The South Pole facet is aligned at 135° west, 45° west, 45° east, or 135° east, respectively, from the central meridian.

12, 13, 14, or 15

The North Pole facet is aligned to the meridian that is 135° east of the central meridian.

The South Pole facet is aligned at 135° west, 45° west, 45° east, or 135° east, respectively, from the central meridian.

## Sources

No available public source.