Skip to main content

Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Table 1 Surface area of objects which the circumscribed sphere (one that touches the polygon at all vertices) has a unitary radius (R=1). The number of vertices N and the number of triangular faces N’ are also shown

From: Implementation and clinical application of a deformation method for fast simulation of biological tissue formed by fibers and fluid

Object N N’ Analytical Equation Analytical Result \( {\displaystyle \sum_{i=1}^N\left|{\overrightarrow{S}}_i\right|} \) \( {\displaystyle \sum_{i=1}^{N^{\prime }}\left|{\overrightarrow{A}}_i\right|} \)
Octahedron 6 8 \( 4\sqrt{3}{R}^2 \) 6.92820 6.92820 6.92820
Icosahedron 12 20 \( {\scriptscriptstyle \frac{40\sqrt{3}}{5+\sqrt{5}}}{R}^2 \) 9.57454 9.57454 9.57454
≈ Sphere 642 1280 ≈ 4πR 2 12.5664 12.5037 12.5065