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# Argument selection for T611
This draft follows numberdb-data family issue #245. The local and live skills
archived in `agents/runs/20261029T183732Z-build-skills/manifest.json` both have
SHA-256 `28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
The archived instructions, rather than the older campaign-gate digest, govern
this build. An independent critique must assess this selection separately.
## Quantity and conventions
Every row is the hyperbolic volume of one polyhedron in sectional curvature
-1, equivalently the covolume of its full face-reflection group. The two
families are arguments of the same volume invariant. There is no second
quantity, manifold-cover volume, rescaling choice, or sampled angle.
## Parameter `family`: discrete_index
`antiprism` denotes the ideal right-angled n-antiprism A_n. Its two n-gonal
bases and 2n triangular lateral faces fix the combinatorial type; the ideal
right-angled realization is unique. Repovš and Vesnin, *On a family of
hyperbolic Brunnian links and their volumes* (2024), Section 2, Figure 4 and
equation (1), specify the objects and their volumes. These polyhedra also
arise in decompositions of link complements (their Theorem 2.1).
`lobell` denotes the compact right-angled Löbell polyhedron L_n. Inoue,
*Organizing volumes of right-angled hyperbolic polyhedra* (2008), Section 4,
defines it by gluing two pentagonal flowers along the boundary to produce a
trivalent sphere. This is stronger than specifying only the face counts.
Theorem 4.1 gives the volume; Theorem 9.1 identifies these polyhedra as the
terminal pieces of volume-decreasing simplifications of compact right-angled
polyhedra. The same notation and normalization are retained throughout.
Both groups are discrete geometric families with the same selection role.
Their combination covers ideal and compact examples without including an
unrelated invariant or a deformation parameter. This is not a reference_sample
of arbitrary input angles. The angular arguments are derived from n.
## Parameter `n`: discrete_index, assessed within each family
For A_n, n is the number of sides of either base, an integer n >= 3. Every
n=3,...,30 is included, beginning with the ideal octahedron and continuing
through 60 ideal vertices and 62 faces.
For L_n, n is the number of sides of either base, an integer n >= 5. Every
n=5,...,30 is included, beginning with the compact right-angled dodecahedron
and continuing through 120 finite vertices and 62 faces. The pentagonal
flower construction determines each object, not an independently chosen
shape or angle.
Thirty is a practical, noncanonical stopping point. Consecutive small and
moderate sizes give useful recognition coverage in both geometric settings,
including the initial named solids, without extending one family's depth
while omitting the other. It is not a mathematical transition or a target
entry count. The initial segments have short 100-digit entries; increasing
n would add more of the same discrete construction rather than a missing
kind of example. No individual fame is required for intermediate n.
## Enumeration and scope
The generator enumerates antiprism n=3,...,30 first, then lobell n=5,...,30,
each in increasing order: 28 + 26 = 54 rows. Its optional maximum argument
permits future extension but the default matches the completeness note.
The parameters state the infinite domains; the note states these finite
bounds and their rationale. There are no hidden reference inputs or Cartesian
products of continuous parameters. Growth rates are a distinct companion
proposal and are not stored here.
## Live-corpus check and tag proposal
Searches for antiprism, Lobell, Löbell and hyperbolic polyhedra, the screening
helpers, and numerical lookups found no duplicate volume family. T85 has
Euclidean Platonic volumes; T224 has simplex volumes; T175 has Clausen values.
Their actual addresses were read and linked. No growth-rate companion existed
at build time, so no address has been invented for it.
The existing tags volume, discrete geometry, groups and period fit. A missing
`hyperbolic geometry` tag would serve this table and T222, T223 and T224, as
well as the planned Löbell growth table. It is proposed for family review;
this build does not edit those published tables or invent a singleton tag.