1. What is the Height of Tetrakis Hexahedron?

The Height of Tetrakis Hexahedron is the vertical distance from any vertex of the Tetrakis Hexahedron to the face which is directly opposite to that vertex. It is an important geometric measurement in this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Tetrakis Hexahedron (m)
• \( r_i \) — Insphere Radius of Tetrakis Hexahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula establishes a direct proportional relationship between the height of the polyhedron and its insphere radius, scaled by the constant factor of √5.

3. Importance of Height Calculation

Details: Calculating the height of a Tetrakis Hexahedron is essential for understanding its spatial dimensions, volume calculations, and for applications in geometry, architecture, and material science where this polyhedral shape is used.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and valid. 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 seen as a cube with square pyramids on each face. It has 24 faces, 14 vertices, and 36 edges.

Q2: What is the insphere radius?
A: The insphere radius 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.

Q3: Why is the constant √5 used in the formula?
A: The constant √5 arises from the geometric relationships and proportions specific to the Tetrakis Hexahedron's structure and symmetry.

Q4: 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 height and insphere radius.

Q5: What are practical applications of this calculation?
A: This calculation is useful in crystallography, architectural design, 3D modeling, and any field that involves working with polyhedral structures.