Truncated Icosidodecahedron Edge Of Hexakis Icosahedron Given Volume Calculator

Formula Used:

\[ le(Truncated\ Icosidodecahedron) = \frac{5}{2 \times \sqrt{15 \times (5 - \sqrt{5})}} \times \left( \frac{88 \times V}{25 \times \sqrt{6 \times (185 + 82 \times \sqrt{5})}} \right)^{\frac{1}{3}} \]

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 mathematical formula:

\[ le = \frac{5}{2 \times \sqrt{15 \times (5 - \sqrt{5})}} \times \left( \frac{88 \times V}{25 \times \sqrt{6 \times (185 + 82 \times \sqrt{5})}} \right)^{\frac{1}{3}} \]

Where:

\( le \) — Truncated Edge of Hexakis Icosahedron (meters)
\( V \) — Volume of Hexakis Icosahedron (cubic meters)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the truncated edge length based on the volume of the Hexakis Icosahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Truncated Edge Calculation

Details: Calculating the truncated edge is essential for geometric analysis, architectural design, and mathematical modeling involving Hexakis Icosahedrons. It helps in understanding the spatial properties and proportions of this complex polyhedral structure.

4. Using the Calculator

Tips: Enter the volume of the Hexakis Icosahedron in cubic meters. The volume must be a positive value 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: How is this formula derived?
A: The formula is derived from geometric relationships and mathematical properties specific to the Hexakis Icosahedron and its relationship with the truncated icosahedron.

Q3: What are typical values for truncated edge length?
A: The truncated edge length varies depending on the volume, but typically ranges from fractions of a meter to several meters for practical applications.

Q4: Can this calculator handle very large or very small volumes?
A: Yes, the calculator can handle a wide range of volume values, though extremely large or small values may be limited by computational precision.

Q5: What practical applications does this calculation have?
A: This calculation is used in geometric modeling, architectural design, crystallography, and various fields that involve complex polyhedral structures.