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Publish the Obsidian vault's Knowledge folder as /knowledge (881 notes, 67 folders), with a Knowledge item in the nav and footer. - scripts/import_knowledge.py regenerates data/knowledge from the vault: slugged paths, folder notes as index pages, wikilinks resolved to site links (or plain text), callouts, highlights, and Dataview tables rendered statically. Personal notes are withheld via an exclusion list plus a privacy guard. - tuftecms/core/knowledge.py builds a concept index from note titles and aliases. First mentions on ordinary pages link to their Knowledge note (capped, never in headings, code, links, or sidenotes); Knowledge pages list related notes and where they're mentioned across the site; other pages get a Related Knowledge block. - Knowledge URLs join sitemap.xml (so the sweep test covers them), never displace existing legacy slugs, list alphabetically, and mermaid diagrams render client-side only on pages that have them.
39 lines
2.2 KiB
Markdown
39 lines
2.2 KiB
Markdown
---
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description: Two pyramids kissing at the base — the shape of balance held in the air.
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source: obsidian-knowledge
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---
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# Octahedron
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> *Two pyramids kissing at the base — the shape of balance held in the air.*
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---
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## The Form
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The octahedron is composed of eight equilateral triangles arranged as two square pyramids joined base to base. It has six vertices and twelve edges, and it possesses a poised, diamond-like symmetry: rest it on a point and it stands in perfect equilibrium, tipped in any direction it would fall. This quality of balance is intrinsic to its geometry. The figure hinges around its central square as if suspended between an upper and a lower world, neither wholly ascending nor wholly descending.
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The octahedron is the dual of the cube, its centers of faces marking the cube's corners and vice versa. Where the cube is seated and solid, the octahedron is light and pivotal, and the two complete one another as a single reciprocal pair. Among sacred forms the octahedron often appears at hinges and transitions, its twin-pyramid shape reading naturally as the meeting place of above and below, the point where opposites are brought into level agreement.
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## Correspondences
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| Attribute | Value |
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|---|---|
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| Faces | 8 |
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| Face shape | Equilateral triangle |
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| Edges | 12 |
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| Vertices | 6 |
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| Element | Air |
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| Dual | Cube |
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## Meaning
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Plato assigned the octahedron to Air, the element that moves freely and mediates between fire and water, heaven and earth. Air is subtle, mobile, and connective, and the octahedron shares those qualities in its poised, balanceable form. In [Alchemy](/knowledge/alchemy) Air is the element of communication and of the volatile spirit rising, the breath that carries transformation between states. The octahedron thus becomes the geometry of equilibrium, mediation, and exchange, the figure that holds tension in graceful suspension. Its twin pyramids, mirror images meeting at a shared plane, offer a small emblem of the reconciled opposite, the still point balanced between two contrary reaches.
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## Related
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- [Platonic Solids](/knowledge/sacred-geometry/platonic-solids)
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- [Cube](/knowledge/sacred-geometry/cube)
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- [Tetrahedron](/knowledge/sacred-geometry/tetrahedron)
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- [Sacred Geometry](/knowledge/sacred-geometry)
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