1. What is the Circumsphere Radius of Truncated Tetrahedron?

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

2. How Does the Calculator Work?

The calculator uses the Circumsphere Radius formula:

Where:

• \( r_c \) — Circumsphere Radius of Truncated Tetrahedron (m)
• \( l_e \) — Edge Length of Truncated Tetrahedron (m)
• \( \sqrt{22} \) — Square root of 22 (approximately 4.69041576)

Explanation: The formula calculates the radius of the sphere that circumscribes the truncated tetrahedron based on its edge length.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry and 3D modeling for understanding the spatial properties of truncated tetrahedrons, determining bounding spheres for collision detection, and analyzing the geometric characteristics of this polyhedron.

4. Using the Calculator

Tips: Enter the edge length of the truncated tetrahedron in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Tetrahedron?
A: A truncated tetrahedron is an Archimedean solid created by truncating the vertices of a regular tetrahedron, resulting in 4 regular hexagonal faces and 4 equilateral triangular faces.

Q2: How is the circumsphere radius different from the insphere radius?
A: The circumsphere radius touches all vertices of the polyhedron, while the insphere radius touches all faces from the inside.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to truncated tetrahedrons. Other polyhedrons have different circumsphere radius formulas.

Q4: What are the practical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, architectural design, and computer graphics for 3D object representation.

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect truncated tetrahedrons and provides precise results when accurate edge length measurements are used.