1. What is Surface to Volume Ratio of Deltoidal Hexecontahedron?

The Surface to Volume Ratio (SA:V) of a Deltoidal Hexecontahedron is a geometric property that relates the total surface area of the polyhedron to its volume. It is an important parameter in materials science and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius (m)
• \( \sqrt{} \) — Square root function

Explanation: The formula calculates the surface to volume ratio based on the insphere radius of the deltoidal hexecontahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemical engineering, and physics. It affects properties like reactivity, heat transfer, and diffusion rates in materials and structures.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a Catalan solid with 60 deltoid faces. It is the dual polyhedron of the rhombicosidodecahedron.

Q2: What does the Surface to Volume Ratio represent?
A: The SA:V ratio indicates how much surface area a structure has relative to its volume, which is important for processes that occur at surfaces.

Q3: What are typical values for SA:V ratio?
A: The SA:V ratio depends on the size and geometry of the polyhedron. Smaller structures generally have higher SA:V ratios.

Q4: What units are used for the calculation?
A: The calculator uses meters for length inputs and returns results in m⁻¹ (reciprocal meters).

Q5: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the deltoidal hexecontahedron geometry.