Circumsphere Radius of Disheptahedron given Midsphere Radius Calculator

Formula Used:

\[ r_c = \frac{2 \times r_m}{\sqrt{3}} \]

Circumsphere Radius of Disheptahedron:

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1. What is the Circumsphere Radius of Disheptahedron?

The Circumsphere Radius of Disheptahedron is the radius of the sphere that contains the Disheptahedron in such a way that all the vertices of the Disheptahedron are touching the sphere. It represents the smallest sphere that can completely enclose the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{2 \times r_m}{\sqrt{3}} \]

Where:

\( r_c \) — Circumsphere Radius of Disheptahedron (m)
\( r_m \) — Midsphere Radius of Disheptahedron (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula establishes a direct mathematical relationship between the midsphere radius and the circumsphere radius of a disheptahedron, using the constant factor of 2/√3.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry and 3D modeling as it helps determine the bounding sphere of a polyhedron, which is crucial for collision detection, spatial analysis, and understanding the spatial properties of geometric shapes.

4. Using the Calculator

Tips: Enter the midsphere radius value in meters. The value must be positive and greater than zero. The calculator will automatically compute the corresponding circumsphere radius.

5. Frequently Asked Questions (FAQ)

Q1: What is a Disheptahedron?
A: A Disheptahedron is a polyhedron with fourteen faces, typically combining triangular and square faces in a specific geometric configuration.

Q2: How is the Midsphere Radius different from Circumsphere Radius?
A: The midsphere radius touches the midpoints of all edges, while the circumsphere radius passes through all vertices of the polyhedron.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to the Disheptahedron geometry. Different polyhedrons have different mathematical relationships between their midsphere and circumsphere radii.

Q4: What are the practical applications of this calculation?
A: This calculation is used in computer graphics, 3D modeling, architectural design, and mathematical research involving polyhedral geometry.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric Disheptahedrons. The accuracy depends on the precision of the input midsphere radius value.