Edge Length of Snub Dodecahedron given Midsphere Radius Calculator

Formula Used:

\[ l_e = \frac{2 \times r_m}{\sqrt{\frac{1}{1 - 0.94315125924}}} \]

Edge Length of Snub Dodecahedron:

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1. What is the Edge Length of Snub Dodecahedron?

The Edge Length of Snub Dodecahedron is the length of any edge of this particular polyhedron. The Snub Dodecahedron is an Archimedean solid with 92 faces (12 pentagons and 80 triangles), 150 edges, and 60 vertices.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ l_e = \frac{2 \times r_m}{\sqrt{\frac{1}{1 - 0.94315125924}}} \]

Where:

\( l_e \) — Edge Length of Snub Dodecahedron (m)
\( r_m \) — Midsphere Radius of Snub Dodecahedron (m)
0.94315125924 — Constant value specific to Snub Dodecahedron geometry

Explanation: This formula establishes the relationship between the midsphere radius and the edge length of a Snub Dodecahedron, using a specific mathematical constant derived from its geometric properties.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the dimensions and proportions of Snub Dodecahedron in various applications including crystallography, architectural design, and mathematical modeling of polyhedral structures.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be a positive number greater than zero. The calculator will compute the corresponding edge length of the Snub Dodecahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Snub Dodecahedron?
A: A Snub Dodecahedron is an Archimedean solid composed of 12 regular pentagons and 80 equilateral triangles, with chiral symmetry.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of a sphere that is tangent to all edges of the polyhedron.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise based on the geometric properties of the Snub Dodecahedron.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula with the constant 0.94315125924 applies only to the Snub Dodecahedron.

Q5: What are practical applications of this calculation?
A: This calculation is useful in fields such as molecular modeling, architectural design, game development, and mathematical research involving polyhedral geometry.