Prefix Meaning "At Most"?

Question

Is there a prefix meaning "at most" or "capped at"? I'd like to describe a spherical cap (Wikipedia, Wolfram) that is at most a hemisphere. The blue solid in the diagram below shows the type of cap I'm comfortable referring to as a subhemispherical cap (a term I just made up to differentiate from the red solid, which is also a spherical cap,) however 'sub-' is strictly less than, whereas I mean to say less than or equal to. I thought of subhemispherical cap or hemisphere, which depicts nicely that a hemispherical cap is in fact a hemisphere, but it does sound somewhat cleaner to call it a subhemi- or hemispherical cap (although the oddity of calling a hemisphere a hemispherical cap makes me prefer the former.) I list hemi- second both times as it is the edge case.

Still, what I really want is to combine the two into one term, i.e. [prefix]hemispherical cap. This would avoid the awkwardness of those phrasings and would be an easily repeatable phrase in a paper.

By the way I do find unfortunate that the word cap here does not fit with the common English usage, synonymous with lid, if it did I could just call it a spherical cap.

Also this has to be easy to understand, if the prefix is too niche I can't use it (although I'd still be curious to hear it.)

EDITED: For extra clarity on what I want, what I came up with, and added an image.

Answer 1

You could say that the cap is within or inside of the hemispherical cap: Endohemispherical cap

End- meaning inside of or within, as in
endorse, endocardial, endergonic, endoskeleton, endoscope, endogenous

Source: https://www.quia.com/files/quia/users/skrichard/ComSkills2/RootsPrefixesSuffixes

Answer 2

Perhaps the language of topology would give you more scope than the language of spherical geometry, e.g.

• The surface of the sphere is a set of points S

• A partial cover of S a collection of subsets that contains
  some but not all of the points in S.

• A bounded partial cover is a collection that satisfies some
  bound, e.g. on the shape, size, number of subsets, or any other
  property one might care to define.

• A hemispherically bounded partial cover would then have the
  properties you are looking for, provided that you define
  "hemispherically bounded" in an earlier step.

This is not a single-word answer, but with such a definition you could then introduce a term of your own, such as a cup cover, and use it within the scope of your document.

I have to confess that this is a somewhat frivolous use of topological language, but it might do the job.

Answer 3

EDIT

Mathematically, you want to say where theta is <= 90 degrees.

By definition, a subset can also contain the entire set. By analogy, a sub-hemispherical cap can include the entire hemisphere. I would state this as a definition before using it.