Edge Length of Small Stellated Dodecahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ l_e = \frac{15 \times \sqrt{5 + 2\sqrt{5}}}{\frac{5}{4} \times (7 + 3\sqrt{5}) \times AV} \]

Edge Length of Small Stellated Dodecahedron:

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1. What is the Edge Length of Small Stellated Dodecahedron?

The Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron. It is a fundamental geometric property used in polyhedral calculations and 3D modeling.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ l_e = \frac{15 \times \sqrt{5 + 2\sqrt{5}}}{\frac{5}{4} \times (7 + 3\sqrt{5}) \times AV} \]

Where:

\( l_e \) — Edge Length of Small Stellated Dodecahedron (m)
\( AV \) — SA:V of Small Stellated Dodecahedron (1/m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the edge length based on the surface area to volume ratio of the Small Stellated Dodecahedron, incorporating mathematical constants related to its geometric properties.

3. Importance of Edge Length Calculation

Details: Accurate edge length calculation is crucial for geometric modeling, architectural design, and mathematical analysis of polyhedral structures. It helps in understanding the spatial properties and proportions of the Small Stellated Dodecahedron.

4. Using the Calculator

Tips: Enter the SA:V ratio in 1/m. The value must be positive and greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Small Stellated Dodecahedron?
A: The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron that represents one of the four regular star polyhedra, formed by extending the faces of a regular dodecahedron.

Q2: What does SA:V ratio represent?
A: SA:V ratio represents the surface area to volume ratio, which is an important geometric property that influences various physical and chemical properties of the shape.

Q3: What are typical values for SA:V ratio?
A: The SA:V ratio depends on the size and proportions of the specific Small Stellated Dodecahedron being measured, with smaller objects generally having higher SA:V ratios.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect geometric shape and may not account for manufacturing tolerances or material properties in physical implementations.

Q5: What units should be used?
A: The calculator uses meters for length and 1/m for SA:V ratio. Ensure consistent units for accurate results.