Let me try a different approach with more precise geometry for the octahedron:
```html
3D Octahedron
```
Changes made:
1. Repositioned faces with more precise translations
2. Adjusted the perspective and initial viewing angle
3. Made the triangles more proportional
4. Separated upper and lower pyramids with clearer transformations
5. Made the color slightly more transparent for better depth perception
Let me know if you still see issues with the rendering and I'll make further adjustments.