Formula Used:
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The midsphere radius of a Triakis Icosahedron is the radius of the sphere that is tangent to all edges of the polyhedron. For a Triakis Icosahedron, which is an icosahedron with triangular pyramids added to each face, this sphere touches each edge at exactly one point.
The calculator uses the formula:
Where:
Explanation: This formula derives from the geometric properties of the Triakis Icosahedron, relating its midsphere radius to its volume through the golden ratio and cubic root relationships.
Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Triakis Icosahedron, including its symmetry and packing characteristics.
Tips: Enter the volume of the Triakis Icosahedron in cubic meters. The volume must be a positive value. The calculator will compute the corresponding midsphere radius.
Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid created by adding a triangular pyramid to each face of a regular icosahedron, resulting in a polyhedron with 60 isosceles triangular faces.
Q2: How is the midsphere different from the insphere?
A: The midsphere is tangent to all edges, while the insphere is tangent to all faces. For most polyhedra, these are different spheres with different radii.
Q3: What are typical values for the midsphere radius?
A: The midsphere radius depends on the volume. For a given volume, the midsphere radius of a Triakis Icosahedron is determined by its specific geometric proportions.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Icosahedron. Other polyhedra have different relationships between volume and midsphere radius.
Q5: What precision does the calculator provide?
A: The calculator provides results with up to 12 decimal places for accuracy in geometric calculations.