A regular octahedron can be symmetrically dissected into equal pyramids with edge, face, and volume center points in four ways. They can be seen as catalan solids with each visible face being connected to the volume center. Moving the edge-division for the deltoidal icositetrahedron can define a chiral octahedral symmetry.
| Pyramids | 8 | 24 | 24 | 48 | |
|---|---|---|---|---|---|
| Symmetry | Oh | O | Oh | ||
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| Catalan | Octahedron | Triakis octahedron | Deltoidal icositetrahedron | Disdyakis dodecahedron | |
| Conway | O | kO | oO | mO | |