Volume of Great Icosahedron given Long Ridge Length Calculator

Formula Used:

\[ V = \frac{25 + 9\sqrt{5}}{4} \times \left( \frac{10 \times l_{\text{Ridge(Long)}}}{\sqrt{2} \times (5 + 3\sqrt{5})} \right)^3 \]

Volume of Great Icosahedron:

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1. What is the Volume of Great Icosahedron?

The Volume of Great Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron. It is a geometric measurement that quantifies the capacity of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{25 + 9\sqrt{5}}{4} \times \left( \frac{10 \times l_{\text{Ridge(Long)}}}{\sqrt{2} \times (5 + 3\sqrt{5})} \right)^3 \]

Where:

\( V \) — Volume of Great Icosahedron (m³)
\( l_{\text{Ridge(Long)}} \) — Long Ridge Length of Great Icosahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)
\( \sqrt{2} \) — Square root of 2 (approximately 1.41421)

Explanation: The formula calculates the volume based on the long ridge length, incorporating mathematical constants and geometric relationships specific to the Great Icosahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes like the Great Icosahedron is fundamental in mathematics, engineering, and architectural design. It helps in understanding spatial properties and material requirements.

4. Using the Calculator

Tips: Enter the Long Ridge Length in meters. The value must be positive and valid. The calculator will compute the volume based on the provided input.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Icosahedron?
A: The Great Icosahedron is a non-convex polyhedron with 20 triangular faces. It is one of the Kepler-Poinsot solids.

Q2: How accurate is this calculation?
A: The calculation is mathematically precise based on the formula, assuming exact input values and proper implementation of mathematical operations.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert the input to meters first or adjust the result accordingly.

Q4: What are typical values for Long Ridge Length?
A: The Long Ridge Length varies based on the specific Great Icosahedron. It should be a positive real number.

Q5: Is this formula applicable to all polyhedra?
A: No, this formula is specific to the Great Icosahedron. Other polyhedra have different volume formulas.