1. What is Volume of Small Stellated Dodecahedron?

The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron with 12 pentagram faces. Its volume represents the total three-dimensional space enclosed by its surface.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Small Stellated Dodecahedron (m³)
• \( h_{Pyramid} \) — Pyramidal Height of Small Stellated Dodecahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the volume based on the pyramidal height, incorporating the mathematical constant √5 which is fundamental to pentagonal geometry.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in mathematics, architecture, and engineering for understanding spatial properties and material requirements.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Small Stellated Dodecahedron?
A: It's one of the four Kepler-Poinsot solids, formed by extending the faces of a regular dodecahedron until they intersect.

Q2: What units should be used for input?
A: The calculator uses meters for length measurements, resulting in cubic meters for volume.

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q4: What is the significance of √5 in the formula?
A: √5 appears frequently in formulas related to pentagonal symmetry and the golden ratio, which are fundamental to dodecahedral geometry.

Q5: Are there other ways to calculate this volume?
A: Yes, the volume can also be calculated using edge length or other dimensional parameters, but this calculator specifically uses pyramidal height.