Equidimensional (geology)

Equidimensional is a term applied to objects that have nearly the same dimensions (i.e. are nearly the same size) in all directions.

In geology

Zingg shape classification map for any solid object's convex envelope, in terms of long (a), intermediate (b) and short (c) envelope axes.

Equidimensional is sometimes used by geologists as a synomym for equant. Deviations from equidimensional are used to classify the shape of convex objects like rocks or particles. For instance Th. Zingg proposed that if a, b and c are the long, intermediate, and short axes of a convex structure, then four mutually exclusive shape classes may be defined by:

Table 1: Zingg's convex object shape classes

shape category	long & intermediate axes	intermediate & short axes	explanation	example
equant	b < a < R b	c < b < R c	all dimensions are comparable	ball
prolate	a > R b	c < b < R c	one dimension is much longer	cigar
oblate	b < a < R b	b > R c	one dimension is much shorter	pancake
bladed	a > R b	b > R c	all dimensions are way different	belt

Here R is a number greater than 1. For Zingg's applications, R was set equal to 3/2.

The relationship between the four categories is illustrated in the figure at right, which allows one to plot long and short axis dimensions for the convex envelope of any solid object. Perfectly equidimensional spheres plot in the lower right corner. Objects with equal short and intermediate axes lie on the upper bound, while objects with equal long and intermediate axes lie on the lower bound.

The point of intersection of all 4 classes on this plot, when R=3/2, occurs when the object's axes a:b:c have ratios of 9:6:4. Make a any longer and the object becomes prolate, make c any shorter and it becomes oblate. Bring all values closer together and it becomes equidimensional, make them all further apart and it becomes bladed. Where is your convex envelope's shape located on this plot?

See Also

• aspect ratio
• prolate
• oblate
• equant