Circumsphere Radius of Truncated Rhombohedron Calculator

Circumsphere Radius of Truncated Rhombohedron Formula:

\[ r_c = \frac{\sqrt{14 - 2\sqrt{5}}}{4} \times \frac{2l_e}{3 - \sqrt{5}} \]

Circumsphere Radius of Truncated Rhombohedron:

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1. What is Circumsphere Radius of Truncated Rhombohedron?

The Circumsphere Radius of a Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere. It represents the distance from the center of the polyhedron to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the Circumsphere Radius formula:

\[ r_c = \frac{\sqrt{14 - 2\sqrt{5}}}{4} \times \frac{2l_e}{3 - \sqrt{5}} \]

Where:

\( r_c \) — Circumsphere Radius of Truncated Rhombohedron (m)
\( l_e \) — Edge Length of Truncated Rhombohedron (m)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the radius of the circumscribed sphere based on the edge length of the truncated rhombohedron, using mathematical constants derived from the geometric properties of the shape.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry and 3D modeling for understanding the spatial dimensions of polyhedra, determining bounding spheres for collision detection, and analyzing the geometric properties of complex shapes.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Rhombohedron?
A: A Truncated Rhombohedron is a polyhedron obtained by truncating the vertices of a rhombohedron, resulting in a shape with both triangular and rhombohedral faces.

Q2: What are the applications of circumsphere radius calculation?
A: This calculation is used in crystallography, molecular modeling, computer graphics, and architectural design where precise spatial relationships of polyhedral shapes are important.

Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect truncated rhombohedrons and provides precise results when correct input values are used.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can convert your measurements to meters before inputting them for accurate results.

Q5: What if I get an error in calculation?
A: Ensure that the input value is a positive number greater than zero. The formula involves square roots and mathematical operations that require valid numerical inputs.