Form Factor:Octahedron

Equations

For a regular octahedron of edge-length 2R

• Volume Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{oct} = \frac{8 \sqrt{2} }{3} R^3}
• Projected (xy) surface area Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Sp = 4R^2}
• Surface area Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_{oct} = 8 \sqrt{3} R^2}

Pyramid

The Octagon shaped can be considered to be formed from two square-based pyramids. Similarly the form factor can be computed from appropriate summation of two pyramid form factors.

See Also

• The chord-length probability density of the regular octahedron S. Ciccariello J. Appl. Cryst. 2014, 47 doi: 10.1107/S1600576714011121