As an example, the Radius of Gyration (Rg) of a Truncated Icosahedron (the shape of the C60-molecule) is being calculated. The polyhedral shape consists of 20 hexagons and 12 pentagons (60 vertices, 32 faces, 90 edges) with an unilateral edge-length

The parameters for the solid shape are entered as input into the Rg-calculator as shown below:

Parameter (Truncated Icosahedron) |
Value |

Volume | 55.288 |

Surface | 72.607 |

Perimeter | 90.000 |

out-sphere radius ro | 2.478 |

mid-sphere radius rm | 2.427 |

in-sphere radius ri (pentagons) | 2.327 |

in-sphere radius ri (hexagons) | 2.267 |

Rg of solid | 1.833 |

Rg of faces | 2.366 |

Rg of edges | 2.444 |

Rg of vertices ( = ro) | 2.478 |

As another example, the Radius of Gyration (Rg) of the Cuboctahedron (CO) and of two of its variations (Octahemioctahedron (OH) and Cubohemioctahedron (CH)) are being calculated. The polyhedral shape consists of 8 trigons and 6 tetragons (12 vertices, 14 faces, 24 edges) with an unilateral edge-length

The parameters for the solid shape are entered as input into the Rg-calculator as shown below:

Parameter (Cuboctahedron) |
Value |

Volume | 2.357 |

Surface | 9.464 |

Perimeter | 24.000 |

out-sphere radius ro | 1.000 |

mid-sphere radius rm | 0.866 |

in-sphere radius ri (trigons) | 0.816 |

in-sphere radius ri (tetragons) | 0.707 |

Rg (CO) | 0.648 |

Rg (OH) | 0.671 |

Rg (CH) | 0.632 |

Next, the Radius of Gyration (Rg) of the Small Rhombicuboctahedron (RCO) and of two of its variations (Small Cubicuboctahedron (CCO) and Small Rhombihexahedron (RH)) are being calculated. The polyhedral shape consists of 8 trigons and 18 tetragons (24 vertices, 26 faces, 48 edges) with an unilateral edge-length

The parameters for the solid shape are entered as input into the Rg-calculator as shown below:

Parameter (Small Rhombicuboctahedron) |
Value |

Volume | 8.714 |

Surface | 21.464 |

Perimeter | 48.000 |

out-sphere radius ro | 1.399 |

mid-sphere radius rm | 1.307 |

in-sphere radius ri (trigons) | 1.274 |

in-sphere radius ri (tetragons) | 1.207 |

Rg (RCO) | 0.991 |

Rg (CCO) | 0.926 |

Rg (RH) | 0.989 |

Last, the Radius of Gyration (Rg) of two variations of the Octahedron (Stella Octangula (SO) and Tetrahemihexahedron (THH)) are being calculated. The polyhedral shape (octahedron) consists of 8 trigons (6 vertices, 8 faces, 12 edges) with an unilateral edge-length

Parameter (Octahedron) |
Value |

Volume | 0.471 |

Surface | 3.464 |

Perimeter | 12.000 |

out-sphere radius ro | 0.707 |

mid-sphere radius rm | 0.500 |

in-sphere radius ri (trigons) | 0.408 |

Rg (O) | 0.387 |

Rg (SO) | 0.592 |

Rg (THH) | 0.387 |