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Icosahedral Edge Length Of Triakis Icosahedron Given Insphere Radius Calculator

Formula Used:

\[ le(Icosahedron) = \frac{4 \times ri}{\sqrt{\frac{10 \times (33 + 13 \times \sqrt{5})}{61}}} \]

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1. What is Icosahedral Edge Length of Triakis Icosahedron?

The Icosahedral Edge Length of Triakis Icosahedron refers to the length of the edges that form the underlying icosahedral structure of a Triakis Icosahedron. It is a fundamental geometric measurement in this polyhedral shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ le(Icosahedron) = \frac{4 \times ri}{\sqrt{\frac{10 \times (33 + 13 \times \sqrt{5})}{61}}} \]

Where:

Explanation: This formula calculates the icosahedral edge length based on the insphere radius, using the mathematical relationship derived from the geometry of the Triakis Icosahedron.

3. Importance of Icosahedral Edge Length Calculation

Details: Calculating the icosahedral edge length is essential for understanding the geometric properties, spatial dimensions, and structural characteristics of Triakis Icosahedrons in mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero for accurate calculation.

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 the insphere radius defined?
A: The insphere radius is the radius of the largest sphere that can be contained within the Triakis Icosahedron, touching all its faces.

Q3: What are typical applications of this calculation?
A: This calculation is used in geometry research, architectural design, molecular modeling, and various engineering applications involving polyhedral structures.

Q4: Are there limitations to this formula?
A: This formula is specifically derived for Triakis Icosahedrons and may not apply to other polyhedral shapes or irregular geometries.

Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, suitable for most mathematical and engineering applications.

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