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 property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Small Stellated Dodecahedron (m)
• \( l_{c(Pentagram)} \) — Pentagram Chord of Small Stellated Dodecahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula relates the edge length of the polyhedron to the chord length of its pentagram faces through the golden ratio constant.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties, surface area, volume, and other dimensional characteristics of the Small Stellated Dodecahedron.

4. Using the Calculator

Tips: Enter the Pentagram Chord value 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: The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron that represents the first stellation of the dodecahedron.

Q2: What is the Pentagram Chord in this context?
A: The Pentagram Chord is the distance between any pair of non-adjacent peak vertices of the pentagram corresponding to the Small Stellated Dodecahedron.

Q3: Why is the golden ratio (√5) involved in this formula?
A: The golden ratio appears naturally in pentagonal symmetry, which is fundamental to dodecahedral structures.

Q4: What are the practical applications of this calculation?
A: This calculation is used in mathematical geometry, architectural design, and the study of polyhedral structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using precise input values, though practical measurements may introduce some error.