1. What is Pyramidal Edge Length of Tetrakis Hexahedron?

The Pyramidal Edge Length of Tetrakis Hexahedron is the length of the line connecting any two adjacent vertices of pyramid of Tetrakis Hexahedron. It is an important geometric measurement in this polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_{pyramid} \) — Pyramidal Edge Length of Tetrakis Hexahedron (m)
• \( r_m \) — Midsphere Radius of Tetrakis Hexahedron (m)

Explanation: This formula calculates the pyramidal edge length based on the midsphere radius of the Tetrakis Hexahedron, using the mathematical constant √2.

3. Importance of Pyramidal Edge Length Calculation

Details: Calculating the pyramidal edge length is crucial for understanding the geometric properties of Tetrakis Hexahedron, including its surface area, volume, and other dimensional relationships in polyhedral geometry.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding pyramidal edge length.

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: 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: Are there other ways to calculate pyramidal edge length?
A: Yes, the pyramidal edge length can also be calculated using other geometric parameters such as the cube edge length or total surface area.

Q4: What are the practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, and 3D modeling where Tetrakis Hexahedron structures 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.