The three dimensional UCS color space is defined by the vertical L+/L– or light vs. dark (lightness) dimension, perpendicular to the horizontal dimensions j+/j– or yellowness vs. blueness, and g+/g– or greenness vs. redness. Thus a j+g+ color will be yellow green and a j+g– color will be orange. For this image library, I have inverted the standard orientation of the g dimension so that values increase from left to right (negative values are on the left).

The spacing among aim colors is defined across all three dimensions of a perceptual color space by the geometry of the cuboctahedron (diagram, below).

cuboctahedral geometry of the osa uniform color scales
lightness is measured on the L+/L– dimension, yellow/blue on the j+/j– dimension and red/green on the g+/g– dimension; rhombohedral stacking of color "atoms" defines a total of seven unique cleavage planes through the color space (labeled on front planes), with additional two cleavage planes (not shown) defined perpendicular to the j and g dimensions. (Note: direction of g+/g– dimension is reversed from standard orientation in all image files.)

 
This rhombohedral solid defines the type of stacking observed in the carbon atoms of a diamond crystal or in the oranges of a fruit stand display. The spacing in all directions is perfectly regular and maximally compact, creating a lattice for color measurement.

The opposing faces or facets of the cuboctahedron define seven cleavage planes through the perceptual color space, and joining cuboctahedrons vertically defines two more planes, perpendicular to the j and g dimensions. The edges of the cuboctahedron define the intersections between two cleavage planes, which form linear uniform color scales.

Each cleavage plane contains all the aim colors whose Ljg coordinates satisfy one of the following nine formulas:

1. L = constant; j,g take any values
a plane perpendicular to the L dimension and parallel to the j and g dimensions, forming a 1:1 square lattice of colors

2. j = constant; L,g take any values
a plane perpendicular to the j dimension and parallel to the L and g dimensions, forming a 1:1.4 rectangular lattice of colors

3. g = constant; L,j take any values
a plane perpendicular to the g dimension and parallel to the L and j dimensions, forming a 1:1.4 rectangular lattice of colors

4. L + j = constant; g takes any values
a plane parallel to the g dimension, at 55° to the j dimension and 35° to the L dimension, forming a 1:1 hexagonal lattice of colors

5. L – j = constant; g takes any values
a plane parallel to the g dimension, at 55° to the j dimension and 35° to the L dimension, forming a 1:1 hexagonal lattice of colors

6. L + g = constant; j takes any values
a plane parallel to the j dimension, at 55° to the g dimension and 35° to the L dimension, forming a 1:1 hexagonal lattice of colors

7. L – g = constant; j takes any values
a plane parallel to the j dimension, at 55° to the g dimension and 35° to the L dimension, forming a 1:1 hexagonal lattice of colors

8. j + g = constant; L takes any values
a plane parallel to the L dimension, at 45° to the j and g dimensions, forming a 1.4:1.4 diagonal square lattice of colors

9. j – g = constant; L takes any values
a plane parallel to the L dimension, at 45° to the j and g dimensions, forming a 1.4:1.4 diagonal square lattice of colors

contains color scales also found in: j = n; g = n; L+j = n; L-j = n; L+g = n; L-g = n; j+g = n; j-g = n

L = –7
L = –6
L = –5
L = –4
L = –3
L = –2*
L = –1*
L = 0*
L = 1*
L = 2*
L = 3
L = 4
L = 5

contains color scales also found in: L = n; g = n; j+g = n; j-g = n

j = –6
j = –5
j = –4
j = –3
j = –2*
j = –1*
j = 0*
j = 1*
j = 2*
j = 3
j = 4
j = 5
j = 6
j = 7
j = 8
j = 9
j = 10
j = 11
j = 12

contains color scales also found in: L = n; j = n; j+g = n; j-g = n

g = –10
g = –9
g = –8
g = –7
g = –6
g = –5
g = –4
g = –3
g = –2*
g = –1*
g = 0*
g = 1*
g = 2*
g = 3
g = 4
g = 5
g = 6

contains color scales also found in: L = n; j = n; L-j = n; L+g = n; L-g = n

contains color scales also found in: L = n; j = n; L+j = n; L+g = n; L-g = n

contains color scales also found in: L = n; g = n; L-g = n; L+j = n; L-j = n

contains color scales also found in: L = n; g = n; L+g = n; L+j = n; L-j = n

contains color scales also found in: L = n; j = n; g = n; L+g = n; L-g = n; L+j = n; L-j = n; j–g = n

contains color scales also found in: L = n; j = n; g = n; L+g = n; L-g = n; L+j = n; L-j = n; j+g = n