1. What is the Tetrakis Hexahedron Height Formula?

The Tetrakis Hexahedron Height Formula calculates the vertical height of a Tetrakis Hexahedron given its midsphere radius. The Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids on each face.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Tetrakis Hexahedron (m)
• \( r_m \) — Midsphere Radius of Tetrakis Hexahedron (m)

Explanation: This formula establishes a direct relationship between the midsphere radius and the height of the Tetrakis Hexahedron, using the mathematical constant √2.

3. Importance of Height Calculation

Details: Calculating the height of a Tetrakis Hexahedron is important in geometry, 3D modeling, and architectural design where this specific polyhedral shape is used. It helps in determining the spatial dimensions and proportions of the solid.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding height of the Tetrakis Hexahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be obtained by adding a square pyramid to each face of a cube. It has 24 faces, 36 edges, and 14 vertices.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different relationships between their midsphere radius and height.

Q4: What are practical applications of this calculation?
A: This calculation is useful in crystallography, architectural design, and 3D computer graphics where Tetrakis Hexahedron shapes are employed.

Q5: How accurate is this formula?
A: The formula is mathematically exact and provides precise results for any valid input value of midsphere radius.