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The Insphere Radius of Triakis Icosahedron is the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touch the sphere. It represents the largest sphere that can fit inside the polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the radius of the inscribed sphere based on the pyramidal edge length of the Triakis Icosahedron, using mathematical constants and geometric relationships.
Details: Calculating the insphere radius is important in geometry and materials science for understanding the packing properties, volume relationships, and spatial characteristics of polyhedral structures.
Tips: Enter the pyramidal edge length in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron, featuring 60 isosceles triangular faces.
Q2: How is the insphere radius different from circumsphere radius?
A: The insphere radius is the radius of the largest sphere that fits inside the polyhedron, while the circumsphere radius is the radius of the smallest sphere that contains the polyhedron.
Q3: What are practical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, architectural design, and any field dealing with polyhedral structures and their geometric properties.
Q4: Are there limitations to this formula?
A: This formula is specifically designed for the Triakis Icosahedron and assumes perfect geometric proportions. It may not apply to distorted or irregular polyhedra.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Triakis Icosahedron, providing precise results based on the input pyramidal edge length.