Circumsphere Radius of Snub Dodecahedron Calculator

Formula Used:

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

Circumsphere Radius of Snub Dodecahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Circumsphere Radius of Snub Dodecahedron?

The Circumsphere Radius of Snub Dodecahedron is the radius of the sphere that contains the Snub Dodecahedron in such a way that all the vertices are lying on the sphere. It is an important geometric property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the circumsphere radius based on the edge length of the snub dodecahedron, using a specific mathematical relationship derived from its geometric properties.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important for understanding the spatial dimensions and geometric properties of the snub dodecahedron. It helps in various applications including 3D modeling, architectural design, and mathematical analysis of polyhedra.

4. Using the Calculator

Tips: Enter the edge length of the snub dodecahedron in meters. The value must be positive and greater than zero. The calculator will compute the circumsphere radius using the established formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Snub Dodecahedron?
A: A snub dodecahedron is an Archimedean solid with 92 faces (12 pentagons and 80 triangles), 150 edges, and 60 vertices.

Q2: Why is there a constant value of 0.94315125924 in the formula?
A: This constant is derived from the specific geometric properties and trigonometric relationships within the snub dodecahedron structure.

Q3: Can this calculator be used for other polyhedra?
A: No, this specific formula is only applicable to the snub dodecahedron. Other polyhedra have different formulas for calculating their circumsphere radii.

Q4: What are the practical applications of this calculation?
A: This calculation is useful in fields such as crystallography, molecular modeling, architecture, and computer graphics where precise geometric measurements are required.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the given formula. The accuracy of the result depends on the precision of the input value.