Volume Of Great Icosahedron Given Short Ridge Length Calculator

Formula Used:

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

Volume of Great Icosahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 represents the capacity of this particular polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Great Icosahedron (m³)
\( l_{\text{Ridge(Short)}} \) — Short Ridge Length of Great Icosahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)
\( \sqrt{10} \) — Square root of 10 (approximately 3.16228)

Explanation: This formula calculates the volume of a Great Icosahedron based on its short ridge length, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for geometric analysis, architectural design, material estimation, and understanding the spatial properties of the Great Icosahedron in various applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four Kepler-Poinsot polyhedra, a non-convex regular polyhedron with intersecting faces.

Q2: How is the Short Ridge Length defined?
A: Short Ridge Length of Great Icosahedron is defined as the maximum vertical distance between the finished bottom level and the finished top height directly above of Great Icosahedron.

Q3: What units should be used for input?
A: The calculator uses meters as the input unit for consistency with the formula. Ensure your measurement is in meters or convert accordingly.

Q4: Are there limitations to this calculation?
A: The formula assumes a perfect geometric shape. Real-world applications may require adjustments for material thickness, construction tolerances, or other practical considerations.

Q5: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the Great Icosahedron. Other polyhedra have different volume formulas based on their unique geometric properties.