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The Insphere Radius of Triakis Tetrahedron is defined as straight line connecting incenter and any point on insphere of Triakis Tetrahedron. It represents the radius of the largest sphere that can be inscribed within the Triakis Tetrahedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct proportional relationship between the insphere radius and midsphere radius of a Triakis Tetrahedron, with a constant factor of \( \frac{3}{\sqrt{11}} \).
Details: Calculating the insphere radius is important for understanding the geometric properties of Triakis Tetrahedrons, particularly in materials science, crystallography, and mathematical modeling where this polyhedral shape appears.
Tips: Enter the midsphere radius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding insphere radius using the established mathematical relationship.
Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that can be constructed by attaching triangular pyramids to each face of a regular tetrahedron.
Q2: How is the insphere radius different from the midsphere radius?
A: The insphere radius is the radius of the sphere inscribed within the polyhedron (touching all faces), while the midsphere radius is the radius of the sphere that touches all edges.
Q3: What are the units for these measurements?
A: Both radii are typically measured in meters (m) or appropriate length units, though the formula works with any consistent unit system.
Q4: Is this formula specific to Triakis Tetrahedrons?
A: Yes, this particular relationship between insphere radius and midsphere radius is specific to the geometry of Triakis Tetrahedrons.
Q5: Can this calculator be used for other polyhedrons?
A: No, this calculator is specifically designed for Triakis Tetrahedrons. Other polyhedrons have different mathematical relationships between their insphere and midsphere radii.