Insphere Radius Of Tetrakis Hexahedron Given Midsphere Radius Calculator

Formula Used:

\[ r_i = \frac{3 \times r_m}{\sqrt{10}} \]

Insphere Radius of Tetrakis Hexahedron:

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1. What is the Insphere Radius of Tetrakis Hexahedron?

The Insphere Radius of Tetrakis Hexahedron is the radius of the sphere that is contained by the Tetrakis Hexahedron in such a way that all the faces just touching the sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{3 \times r_m}{\sqrt{10}} \]

Where:

\( r_i \) — Insphere Radius of Tetrakis Hexahedron (m)
\( r_m \) — Midsphere Radius of Tetrakis Hexahedron (m)

Explanation: This formula calculates the insphere radius from the given midsphere radius using a constant ratio of 3/√10.

3. Importance of Insphere Radius Calculation

Details: The insphere radius is important in geometry and 3D modeling as it represents the largest sphere that can fit inside the Tetrakis Hexahedron, touching all its faces.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero.

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.

Q2: What is the relationship between insphere and midsphere radii?
A: The insphere radius is always 3/√10 times the midsphere radius for a Tetrakis Hexahedron.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron due to its unique geometric properties.

Q4: What are the units for these measurements?
A: Both radii are typically measured in meters, but any consistent length unit can be used.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Tetrakis Hexahedron shape.