Truncated Icosidodecahedron Edge of Hexakis Icosahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ le = \frac{5}{2\sqrt{15(5-\sqrt{5})}} \times \frac{\frac{6}{5}\sqrt{10(417+107\sqrt{5})}}{RA/V \times \sqrt{6(185+82\sqrt{5})}} \]

Truncated Edge of Hexakis Icosahedron:

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1. What is Truncated Edge of Hexakis Icosahedron?

The Truncated Edge of Hexakis Icosahedron is the length of the edges of a Hexakis Icosahedron that is created by truncating the vertices of an Icosidodecahedron. It represents a specific geometric measurement in this complex polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ le = \frac{5}{2\sqrt{15(5-\sqrt{5})}} \times \frac{\frac{6}{5}\sqrt{10(417+107\sqrt{5})}}{RA/V \times \sqrt{6(185+82\sqrt{5})}} \]

Where:

\( le \) — Truncated Edge of Hexakis Icosahedron (m)
\( RA/V \) — Surface to Volume Ratio (1/m)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the truncated edge length based on the surface to volume ratio of the Hexakis Icosahedron, incorporating various mathematical constants and operations.

3. Importance of Truncated Edge Calculation

Details: Calculating the truncated edge is important in geometric modeling, architectural design, and mathematical research involving complex polyhedra. It helps in understanding the spatial properties and proportions of these intricate structures.

4. Using the Calculator

Tips: Enter the surface to volume ratio value in 1/m. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated icosahedron, featuring 120 faces, 180 edges, and 62 vertices.

Q2: What is the significance of the surface to volume ratio?
A: The surface to volume ratio is an important geometric property that influences various physical characteristics of a shape, including heat transfer, chemical reactivity, and structural stability.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, assuming accurate input values and proper implementation of the mathematical operations.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for calculating the truncated edge of a Hexakis Icosahedron based on its surface to volume ratio.

Q5: What are practical applications of this calculation?
A: Applications include architectural design, molecular modeling, computer graphics, and mathematical research involving complex geometric structures.