Home
Back
Formula Used:
| From: | To: |
The Insphere Radius of a Triakis Octahedron is the radius of the sphere that is contained by the Triakis Octahedron in such a way that all the faces are touching the sphere. It represents the largest sphere that can fit inside the polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula relates the insphere radius to the midsphere radius through a constant factor derived from the geometric properties of the Triakis Octahedron.
Details: Calculating the insphere radius is important in geometry and material science for understanding the spatial properties of polyhedra, packing efficiency, and in applications involving inscribed spheres within complex shapes.
Tips: Enter the midsphere radius value in meters. The value must be positive and valid. The calculator will compute the corresponding insphere radius using the established geometric relationship.
Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that is the dual of the truncated cube. It has 24 isosceles triangular faces, 14 vertices, and 36 edges.
Q2: How is the insphere radius different from the midsphere radius?
A: The insphere radius is the radius of the sphere tangent to all faces, while the midsphere radius is the radius of the sphere tangent to all edges of the polyhedron.
Q3: What are the applications of this calculation?
A: This calculation is used in crystallography, materials science, and 3D modeling where precise geometric measurements of polyhedra are required.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Octahedron. Other polyhedra have different relationships between their insphere and midsphere radii.
Q5: What is the precision of this calculation?
A: The calculation provides a precise mathematical relationship. The practical precision depends on the accuracy of the input midsphere radius measurement.