Volume of Rhombic Dodecahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ V = \frac{16\sqrt{3}}{9} \times \left( \frac{9\sqrt{2}}{2\sqrt{3} \times \frac{S}{V}} \right)^3 \]

Volume of Rhombic Dodecahedron (V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Volume of Rhombic Dodecahedron?

The Volume of Rhombic Dodecahedron is defined as the quantity of three dimensional space enclosed by the entire surface of Rhombic Dodecahedron. It is a polyhedron with 12 congruent rhombic faces, 14 vertices, and 24 edges.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{16\sqrt{3}}{9} \times \left( \frac{9\sqrt{2}}{2\sqrt{3} \times \frac{S}{V}} \right)^3 \]

Where:

\( V \) — Volume of Rhombic Dodecahedron (m³)
\( \frac{S}{V} \) — Surface to Volume Ratio (m⁻¹)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula calculates the volume of a rhombic dodecahedron based on its surface to volume ratio, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in various fields including mathematics, engineering, architecture, and materials science. For rhombic dodecahedrons specifically, volume calculations are important in crystallography, packaging optimization, and structural design.

4. Using the Calculator

Tips: Enter the surface to volume ratio in m⁻¹. The value must be positive and greater than zero. The calculator will compute the corresponding volume of the rhombic dodecahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a rhombic dodecahedron?
A: A rhombic dodecahedron is a polyhedron with 12 congruent rhombic faces. It is a Catalan solid and the dual polyhedron of the cuboctahedron.

Q2: Where are rhombic dodecahedrons found in nature?
A: Rhombic dodecahedral structures appear in crystal formations, particularly in some types of garnet crystals, and in the arrangement of cells in beehives.

Q3: What are practical applications of this calculation?
A: This calculation is used in materials science for crystal volume determination, in engineering for optimal packing problems, and in architecture for space-efficient structural designs.

Q4: How accurate is this formula?
A: The formula is mathematically exact for perfect rhombic dodecahedrons. The accuracy of the result depends on the precision of the input surface to volume ratio value.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the base unit. For other units, convert your surface to volume ratio to m⁻¹ before calculation, and interpret the volume result accordingly.