Home Back

Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius Calculator

Formula Used:

\[ SA:V = \frac{3 \times (1 + \sqrt{3} + \sqrt{5 + (2 \times \sqrt{5})})}{\frac{r_c}{\sqrt{31 + (12 \times \sqrt{5})}} \times (19 + (10 \times \sqrt{5})))} \]

m

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is Surface to Volume Ratio of Truncated Icosidodecahedron?

The Surface to Volume Ratio (SA:V) of a Truncated Icosidodecahedron is the numerical ratio of its total surface area to its volume. It's an important geometric property that describes how much surface area is available per unit volume of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ SA:V = \frac{3 \times (1 + \sqrt{3} + \sqrt{5 + (2 \times \sqrt{5})})}{\frac{r_c}{\sqrt{31 + (12 \times \sqrt{5})}} \times (19 + (10 \times \sqrt{5})))} \]

Where:

Explanation: This formula calculates the surface to volume ratio based on the circumsphere radius of the truncated icosidodecahedron, incorporating various mathematical constants and square roots that characterize this specific polyhedron.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. For polyhedra like the truncated icosidodecahedron, this ratio helps understand properties related to surface interactions, heat transfer, and structural efficiency.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid. The calculator will compute the surface to volume ratio using the specialized formula for truncated icosidodecahedrons.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Icosidodecahedron?
A: A truncated icosidodecahedron is an Archimedean solid with 62 faces (30 squares, 20 regular hexagons, and 12 regular decagons), 180 edges, and 120 vertices.

Q2: Why is the circumsphere radius used in this calculation?
A: The circumsphere radius provides a fundamental geometric reference point that allows for consistent calculation of the surface to volume ratio across different sizes of the polyhedron.

Q3: What are typical values for surface to volume ratio?
A: The SA:V ratio depends on the size of the polyhedron. Smaller polyhedra have higher SA:V ratios, while larger ones have lower ratios.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for truncated icosidodecahedrons. Other polyhedra have different formulas for calculating surface to volume ratios.

Q5: What practical applications does this calculation have?
A: This calculation is useful in crystallography, nanotechnology, architectural design, and any field where the geometric properties of complex polyhedra need to be analyzed.

Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius Calculator© - All Rights Reserved 2025