1. What is the Insphere Radius of Triakis Icosahedron?

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.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius (m)
• \( l_e \) — Icosahedral Edge Length (m)

Explanation: The formula calculates the radius of the inscribed sphere based on the edge length of the underlying icosahedron structure.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and material science for understanding the spatial properties of polyhedra and their packing efficiency.

4. Using the Calculator

Tips: Enter the icosahedral edge length in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

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 this different from a regular icosahedron?
A: While both are polyhedra, the Triakis Icosahedron has triangular faces and different symmetry properties compared to the regular icosahedron.

Q3: What are the practical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, and architectural design where precise geometric properties are required.

Q4: Are there limitations to this formula?
A: This formula is specific to the Triakis Icosahedron geometry and assumes perfect mathematical form without manufacturing tolerances.

Q5: Can this be used for volume calculations?
A: While related, the insphere radius is different from volume calculations, though both are important geometric properties of polyhedra.