1. What is Surface to Volume Ratio of Great Stellated Dodecahedron?

The Surface to Volume Ratio (SA:V) of a Great Stellated Dodecahedron is a geometric property that represents the ratio of its total surface area to its volume. It's an important parameter in various mathematical and physical applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sqrt{} \) — Square root function
• \( Pentagram\ Chord \) — Distance between non-adjacent peak vertices of the pentagram (in meters)

Explanation: This formula calculates the surface to volume ratio based on the pentagram chord length of the Great Stellated Dodecahedron.

3. Importance of SA:V Calculation

Details: The surface to volume ratio is crucial in geometry, materials science, and various engineering applications where the relationship between surface area and volume affects physical properties and behavior.

4. Using the Calculator

Tips: Enter the pentagram chord length in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Stellated Dodecahedron?
A: It's a Kepler-Poinsot polyhedron with 12 pentagrammic faces, 20 vertices, and 30 edges, formed by stellating a regular dodecahedron.

Q2: What is the pentagram chord?
A: The pentagram chord is the distance between any pair of non-adjacent peak vertices of the pentagram that forms the faces of the Great Stellated Dodecahedron.

Q3: What units are used for the SA:V ratio?
A: The SA:V ratio is expressed in reciprocal meters (m⁻¹), as it represents surface area per unit volume.

Q4: Are there other ways to calculate SA:V for this shape?
A: Yes, the SA:V can also be calculated using other geometric parameters such as edge length or circumradius, but the pentagram chord provides a specific approach.

Q5: What applications use SA:V ratios?
A: SA:V ratios are important in heat transfer, chemical reactions, materials science, and biological systems where surface area affects interaction rates.