Short Ridge Length Of Great Icosahedron Given Surface To Volume Ratio Calculator

Formula Used:

\[ l_{Ridge(Short)} = \frac{\sqrt{10}}{5} \times \frac{3\sqrt{3}(5+4\sqrt{5})}{\frac{1}{4}(25+9\sqrt{5}) \times \frac{RA}{V}} \]

Short Ridge Length of Great Icosahedron:

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1. What is Short Ridge Length of Great Icosahedron?

The 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. It's an important geometric measurement in understanding the structure of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Ridge(Short)} = \frac{\sqrt{10}}{5} \times \frac{3\sqrt{3}(5+4\sqrt{5})}{\frac{1}{4}(25+9\sqrt{5}) \times \frac{RA}{V}} \]

Where:

\( l_{Ridge(Short)} \) — Short Ridge Length of Great Icosahedron (m)
\( \frac{RA}{V} \) — Surface to Volume Ratio of Great Icosahedron (1/m)

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

3. Importance of Short Ridge Length Calculation

Details: Calculating the short ridge length is essential for understanding the geometric properties of the Great Icosahedron, which has applications in mathematics, architecture, and molecular modeling.

4. Using the Calculator

Tips: Enter the surface to volume ratio of the Great Icosahedron in 1/m. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four regular star polyhedra, composed of 20 triangular faces that intersect each other.

Q2: How is the surface to volume ratio typically measured?
A: The surface to volume ratio is calculated by dividing the total surface area by the volume of the polyhedron.

Q3: What are typical values for short ridge length?
A: The short ridge length varies depending on the size of the Great Icosahedron, but it's typically in proportion to other dimensions of the shape.

Q4: Are there practical applications for this calculation?
A: Yes, understanding these geometric properties has applications in crystallography, architectural design, and mathematical modeling.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula is derived specifically for the Great Icosahedron due to its unique geometric properties.