Ridge Length of Great Stellated Dodecahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ l_{Ridge} = \frac{1+\sqrt{5}}{2} \times \frac{15\sqrt{5+2\sqrt{5}}}{\frac{5}{4}(3+\sqrt{5}) \times AV} \]

Ridge Length of Great Stellated Dodecahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Ridge Length of Great Stellated Dodecahedron?

The Ridge Length of Great Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron. It is an important geometric measurement in this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ l_{Ridge} = \frac{1+\sqrt{5}}{2} \times \frac{15\sqrt{5+2\sqrt{5}}}{\frac{5}{4}(3+\sqrt{5}) \times AV} \]

Where:

\( l_{Ridge} \) — Ridge Length of Great Stellated Dodecahedron (meters)
\( AV \) — SA:V of Great Stellated Dodecahedron (1/meter)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the ridge length based on the surface area to volume ratio of the Great Stellated Dodecahedron, incorporating the golden ratio and geometric properties of the shape.

3. Importance of Ridge Length Calculation

Details: Calculating the ridge length is essential for understanding the geometric properties, structural integrity, and mathematical relationships within the Great Stellated Dodecahedron, which has applications in geometry, architecture, and mathematical modeling.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the Great Stellated Dodecahedron?
A: The Great Stellated Dodecahedron is one of the Kepler-Poinsot polyhedra, consisting of 12 pentagram faces with each vertex connecting three pentagrams.

Q2: What does SA:V ratio represent?
A: SA:V ratio (Surface Area to Volume Ratio) represents the amount of surface area per unit volume of the polyhedron, which is important for various physical and geometric properties.

Q3: What are typical values for SA:V ratio?
A: The SA:V ratio depends on the size and specific dimensions of the Great Stellated Dodecahedron, with smaller polyhedra having larger ratios and vice versa.

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 are used in this calculation?
A: The ridge length is calculated in meters, and the SA:V ratio is in 1/meter. Ensure consistent units for accurate results.