Circumsphere Radius of Truncated Rhombohedron Given Triangular Edge Length Calculator

Formula Used:

\[ r_c = \frac{\sqrt{14 - 2\sqrt{5}}}{4} \times \frac{l_{e(Triangle)}}{\sqrt{5 - 2\sqrt{5}}} \]

Circumsphere Radius (r_c):

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1. What is the 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 is an important geometric property in three-dimensional geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{\sqrt{14 - 2\sqrt{5}}}{4} \times \frac{l_{e(Triangle)}}{\sqrt{5 - 2\sqrt{5}}} \]

Where:

\( r_c \) — Circumsphere Radius (m)
\( l_{e(Triangle)} \) — Triangular Edge Length of Truncated Rhombohedron (m)

Explanation: This formula calculates the circumsphere radius based on the triangular edge length of the truncated rhombohedron, using mathematical constants and square root functions.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is crucial for understanding the spatial properties and dimensions of truncated rhombohedrons in geometric analysis and 3D modeling applications.

4. Using the Calculator

Tips: Enter the triangular edge length in meters. The value must be positive and valid for accurate calculation.

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 other polygonal faces.

Q2: Why is the circumsphere radius important?
A: The circumsphere radius helps determine the smallest sphere that can completely contain the truncated rhombohedron, which is useful in various geometric and engineering applications.

Q3: What units should be used for input?
A: The calculator uses meters as the unit of measurement for both input and output values.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect geometric shape and may not account for manufacturing tolerances or material deformations in real-world applications.

Q5: Can this formula be used for other polyhedrons?
A: No, this specific formula is derived for truncated rhombohedrons and may not be applicable to other polyhedral shapes.