IE–TE–023 STL GEOMETRIC ANALYSIS =================================== Source file ----------- Filename: ie-te-023.STL Format: binary STL Envelope: 25.4000 × 25.4000 × 25.4000 mm Center: (12.7000, 12.7000, 12.7000) mm The 25.4 mm envelope is exactly one inch. Coordinates occur at 0, 6.35, 12.7, 19.05, and 25.4 mm — a quarter-inch grid. Mesh inventory -------------- Unique vertices: 26 Triangle faces: 32 Unique triangulation edges: 60 Edge-connected face components: 9 Watertight: False Vertex orbits under octahedral symmetry --------------------------------------- 6 vertices: face centers of the one-inch cube; these are the vertices of the central regular octahedron. 8 vertices: cube corners; these are the outer spike tips and also the vertices used by a stella octangula. 12 vertices: permutations of (±1/2, ±1/2, 0) after centering and normalization. They are the midpoints of the central octahedron's 12 edges and simultaneously the vertices of a half-scale cuboctahedron. Face decomposition ------------------ 8 equilateral triangles form a complete central regular octahedron. 24 isosceles triangles form the lateral surfaces of 8 congruent triangular pyramids, 3 faces per pyramid. Each pyramid points along one cube body diagonal and is based on the medial triangle inside one octahedron face. The 8 medial base triangles are absent from the STL. Their edges lie inside the large octahedron faces, but the large faces are not subdivided or welded to them. This explains the non-watertight, 9-component topology. Exact length hierarchy ---------------------- Short medial/cuboctahedral edge: 8.980256 mm Spike lateral edge: 15.554258 mm Central octahedron edge: 17.960512 mm Normalized ratio: 1 : sqrt(3) : 2 Working identification ---------------------- The most defensible descriptive name is: medially stellated octahedral cell or, more explicitly: regular octahedron with eight elongated triangular pyramids on face-medial triangles It is strongly related to both the octet truss cell and the stella octangula, but it is not exactly either standard form: • A regular octet-truss repeating cell has a central regular octahedron with regular tetrahedra connected to all eight full octahedron faces, using equal-length members. • A classic stella octangula is the compound of two regular tetrahedra. In the same coordinate frame its outer tips are the eight cube corners and its central intersection is an octahedron. • In this STL, the outer modules connect to edge-midpoint medial triangles instead of the three full vertices of each octahedron face. Their lateral edges are therefore sqrt(3) times their base edge, not equal to it. Animation controls ------------------ The included HTML is self-contained and uses no CDN or external library. Morph to regular octet: Expands each medial base edge to the corresponding full edge of the octahedron face, revealing the canonical regular tetrahedral connection. Explode spike modules: Moves the eight triangular-pyramid modules outward along the eight cube body diagonals. Cuboctahedral shell: Shows the 12 edge-midpoint vertices and their 24 cuboctahedron edges. Regular octet cell: Shows the central octahedron plus equal-length face-to-corner struts. Stella octangula: Shows the two tetrahedra formed by the two parity classes of cube corners. Repeating matrix: Replicates the source wire cell around the origin for deep-zoom exploration. Naming caution -------------- No source provenance or canonical catalog name was embedded in the STL, and a search for the filename did not locate an authoritative listing. “Medially stellated octahedral cell” is therefore a precise descriptive identification, not a claimed official name.