Midsphere Radius of Tetrakis Hexahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ r_m = \frac{1}{\sqrt{2}} \times \frac{2\sqrt{5}}{RA/V} \]

Midsphere Radius (rₘ):

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1. What is Midsphere Radius of Tetrakis Hexahedron?

The Midsphere Radius of Tetrakis Hexahedron is the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere. It represents the sphere that touches all the edges of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{1}{\sqrt{2}} \times \frac{2\sqrt{5}}{RA/V} \]

Where:

\( r_m \) — Midsphere Radius (m)
\( RA/V \) — Surface to Volume Ratio (1/m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{5} \) — Square root of 5 (approximately 2.2361)

Explanation: This formula calculates the midsphere radius based on the surface to volume ratio of the Tetrakis Hexahedron, using mathematical constants and geometric relationships.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Tetrakis Hexahedron. It helps in determining the sphere that perfectly fits within the polyhedron's edges.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and valid for accurate calculation of the midsphere radius.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids on each face. It has 24 faces, 36 edges, and 14 vertices.

Q2: How is surface to volume ratio defined?
A: Surface to volume ratio is the numerical ratio of the total surface area of a solid to its volume, measured in 1/m.

Q3: What are typical values for midsphere radius?
A: The midsphere radius varies depending on the size and proportions of the Tetrakis Hexahedron, typically ranging from centimeters to meters in practical applications.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different formulas for calculating their midsphere radii.

Q5: What are the applications of midsphere radius calculation?
A: Applications include 3D modeling, computer graphics, architectural design, and mathematical research involving polyhedral geometry.