1. What is the Edge Length of Small Stellated Dodecahedron?

The Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron. It is a fundamental geometric measurement used in polyhedral studies and 3D modeling.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Pyramidal Height — Height of the tetrahedral pyramid (m)

Explanation: This formula calculates the edge length based on the pyramidal height using mathematical constants derived from the geometric properties of the small stellated dodecahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties, surface area, volume, and other characteristics of the small stellated dodecahedron in mathematical and architectural applications.

4. Using the Calculator

Tips: Enter the pyramidal height in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Small Stellated Dodecahedron?
A: It's a Kepler-Poinsot polyhedron with 12 pentagram faces, representing one of the four regular star polyhedra.

Q2: What units should be used for input?
A: The calculator uses meters as the unit of measurement for both input and output values.

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 mathematical significance of √5 in the formula?
A: √5 (square root of 5) is a mathematical constant that appears frequently in formulas related to pentagonal symmetry and golden ratio geometry.

Q5: Are there any limitations to this calculation?
A: This formula is specifically designed for the small stellated dodecahedron and may not apply to other polyhedra or geometric shapes.