Octahedral core
Six axis-aligned vertices complete the central regular octahedron.
±X · ±Y · ±ZSTL artifact · Source geometry / transformation / comparison
IE–TE–023
Medial Stellation.
A one-inch octahedral study composed of a complete central octahedron and eight elongated triangular spike modules—each rising from a face-medial triangle rather than the full face.
The supplied analyzer lets the source model unfold into its vertex orbits, cuboctahedral shell, regular octet cell, stella octangula comparison, and repeating matrix. The page preserves the source while making its geometric identity—and its limits—explicit.
Open the instrument
25.4 mm exact cubic envelope
26 unique vertices
32 triangular faces
1 : √3 : 2 edge-length hierarchy
01 / Interactive instrument
Turn one source
through five readings.
The original self-contained WebGL analyzer is mounted intact below. No external rendering library is required; the mesh and transformation logic remain bundled with the exhibit.
02 / Geometric identity
Three vertex orbits.
One octahedral symmetry.
The 26 vertices separate cleanly under octahedral symmetry. That decomposition is the most direct key to reading the model.
Outer tips
Eight corner positions form the terminal points of the eight spike modules.
All sign triplesCuboctahedral shell
Twelve permutations of two half-coordinates and one zero define a half-scale cuboctahedron.
(±½, ±½, 0)Vertex decomposition6 + 8 + 12 = 26
Octahedron + cube-corner tips + cuboctahedral edge-midpoint shell
03 / Mesh construction
A complete core.
Eight open modules.
8 equilateral faces
The central octahedron is complete and regular.
8 × 3 lateral faces
Each congruent spike is an elongated triangular pyramid represented by three isosceles lateral triangles.
8 medial bases absent
The triangular base of each spike is not included as a face, which is why the exported surface is not watertight.
9 face components
The source triangulation resolves into one central shell plus eight congruent spike components.
Source edge classes
A harmonic metric hidden in the triangulation.
Three edge lengths recur throughout the mesh. Normalized by the shortest class, their relationship is exact within the recovered coordinate model.
8.980256mm115.554258mm√317.960512mm2
04 / Comparative reading
Related forms.
Not interchangeable names.
The analyzer places the source beside two familiar octahedral constructions. Resemblance is useful here, but it is not identity.
Medially stellated octahedral cell
Eight elongated spikes rise from the medial triangle of each octahedron face. Their lateral edges are √3 times the medial base edge.
Best descriptive working nameRegular octet truss
The octet truss alternates regular tetrahedra and octahedra with an equal-member triangulated network. IE–TE–023 is related to this family but is not an equal-member octet cell.
Related lattice logicStella octangula
The classic stella octangula is the compound of two regular tetrahedra. Its eight tips align with the source’s cube-corner orbit, but its construction and proportions differ.
Related outer symmetry05 / Evidence boundary
Preserve the object.
Label the inference.
“Medially stellated octahedral cell” is a defensible descriptive name, not a recovered canonical title.
The model’s dimensions, vertex coordinates, face counts, component structure, symmetry orbits, and edge ratios come from the supplied STL analysis. The octet-truss and stella-octangula views are comparative transformations used to clarify relationships.
Any energetic, cosmological, or metaphysical significance belongs to a subsequent interpretive layer. The geometry can organize that inquiry; it does not, by resemblance alone, prove a physical theory.