Insphere Radius of Tetrakis Hexahedron Calculator

Formula:

\[ r_i = \frac{3}{10} \times l_{e(Cube)} \times \sqrt{5} \]

Insphere Radius of Tetrakis Hexahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 touch the sphere. It represents the largest sphere that can fit inside the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{3}{10} \times l_{e(Cube)} \times \sqrt{5} \]

Where:

\( r_i \) — Insphere Radius of Tetrakis Hexahedron (m)
\( l_{e(Cube)} \) — Cubical Edge Length of Tetrakis Hexahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the radius of the inscribed sphere based on the cube edge length of the Tetrakis Hexahedron, using a constant factor of 3/10 and the square root of 5.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and material science for understanding the spatial properties of the Tetrakis Hexahedron, including its packing efficiency and internal volume characteristics.

4. Using the Calculator

Tips: Enter the cubical edge length of the Tetrakis Hexahedron 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. It has 24 isosceles triangular faces.

Q2: How is the insphere radius different from the circumsphere radius?
A: The insphere radius is the radius of the sphere inscribed inside the polyhedron (touching all faces), while the circumsphere radius is the radius of the sphere that circumscribes the polyhedron (passing through all vertices).

Q3: What are the applications of this calculation?
A: This calculation is used in crystallography, architecture, and 3D modeling where Tetrakis Hexahedron structures appear, helping to determine material properties and spatial relationships.

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 insphere radii.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Tetrakis Hexahedron. The accuracy in practical applications depends on the precision of the input measurements.