Is “symmetricity” a word?

Tiger, Tiger: Symmetricity, Symmetricality, or Symmetricalness?

It doesn't really matter whether this or that dictionary includes or omits it. It is the regular product of applying productive derivational morphology to a basic English word for conversion purposes.

It doesn’t matter whether you use symmetricity, symmetricality, or symmetricalness — any native speaker and indeed any competent second-language user will know exactly what you mean by your term.

This is because you’ve used a basic vocabulary term, the adjective symmetric, and applyied standard suffixes to convert that adjective into a substantive.

The Mathematics of Nominalization Doubly Applied

However, careful writers will wonder why you used a noun-making suffix on an adjective which was itself already the product of someone else applying an adjective-making suffix to. In other words, this math is overly complicated:

adjective₁ = noun₁      + adjective-making suffix
noun₂      = adjective₁ + noun-making      suffix
noun₂      = noun₁      + adjective-making suffix + noun-making suffix

Seems to me you should use noun₁ in the first place instead of adding two suffixes to it to make noun₂.

What’s the original noun, you ask? That would be symmetry.

_{Tiger, tiger, burning bright
In the forests of the night,
What immortal hand or eye
Dare frame thy fearful symmetry?}