Medium Edge Of Hexakis Icosahedron Given Volume Calculator

Formula Used:

\[ l_{medium} = \frac{3}{22} \times (4 + \sqrt{5}) \times \left( \frac{88 \times V}{25 \times \sqrt{6 \times (185 + 82 \times \sqrt{5})}} \right)^{\frac{1}{3}} \]

Medium Edge of Hexakis Icosahedron:

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1. What is the Medium Edge of Hexakis Icosahedron?

The Medium Edge of Hexakis Icosahedron is the length of the edge that connects two non-adjacent and non-opposite vertices of the Hexakis Icosahedron. It is one of the three distinct edge lengths in this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{medium} = \frac{3}{22} \times (4 + \sqrt{5}) \times \left( \frac{88 \times V}{25 \times \sqrt{6 \times (185 + 82 \times \sqrt{5})}} \right)^{\frac{1}{3}} \]

Where:

\( l_{medium} \) — Medium edge length (meters)
\( V \) — Volume of Hexakis Icosahedron (cubic meters)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives the medium edge length from the volume of the Hexakis Icosahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge is essential for understanding the geometric properties of the Hexakis Icosahedron, including its symmetry, surface area, and other dimensional characteristics.

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 dodecahedron. It has 120 faces, 180 edges, and 62 vertices.

Q2: How many different edge lengths does a Hexakis Icosahedron have?
A: A Hexakis Icosahedron has three distinct edge lengths: short, medium, and long edges.

Q3: What are typical applications of this calculation?
A: This calculation is used in geometry research, 3D modeling, architectural design, and materials science where precise polyhedral measurements are required.

Q4: What is the precision of this calculation?
A: The calculator provides results with 6 decimal places precision, suitable for most geometric applications.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Hexakis Icosahedron due to its unique geometric properties.