Volume of Rhombic Dodecahedron given Insphere Radius Calculator

Volume of Rhombic Dodecahedron Formula:

\[ V = 4 \times \sqrt{2} \times r_i^3 \]

Volume of Rhombic Dodecahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is 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:

\[ V = 4 \times \sqrt{2} \times r_i^3 \]

Where:

\( V \) — Volume of Rhombic Dodecahedron (m³)
\( r_i \) — Insphere Radius of Rhombic Dodecahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the volume of a rhombic dodecahedron based on the radius of its inscribed sphere (insphere).

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. For rhombic dodecahedrons, volume calculation is particularly important in crystallography, materials science, and structural design applications.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero. The calculator will compute the volume using the formula V = 4 × √2 × ri³.

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 the dual polyhedron of the cuboctahedron and occurs naturally in some crystal structures.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can be inscribed within the polyhedron, touching all its faces.

Q3: Can this formula be used for any rhombic dodecahedron?
A: Yes, this formula applies to all regular rhombic dodecahedrons where all faces are congruent rhombi.

Q4: What are the practical applications of rhombic dodecahedrons?
A: Rhombic dodecahedrons are used in crystallography (garnet crystal structure), space filling problems, architectural design, and as dice in some tabletop games.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal rhombic dodecahedrons. The accuracy depends on the precision of the input insphere radius measurement.