Cubical Edge Length Of Tetrakis Hexahedron Given Midsphere Radius Calculator

Formula Used:

\[ l_{e(Cube)} = \sqrt{2} \times r_{m} \]

Cubical Edge Length of Tetrakis Hexahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Cubical Edge Length of Tetrakis Hexahedron?

The Cubical Edge Length of Tetrakis Hexahedron is the length of the line connecting any two adjacent vertices of cube of Tetrakis Hexahedron. It is an important geometric measurement in the study of this particular polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{e(Cube)} = \sqrt{2} \times r_{m} \]

Where:

\( l_{e(Cube)} \) — Cubical Edge Length of Tetrakis Hexahedron (m)
\( r_{m} \) — Midsphere Radius of Tetrakis Hexahedron (m)

Explanation: This formula establishes a direct mathematical relationship between the midsphere radius and the cubical edge length of the Tetrakis Hexahedron, with the square root of 2 serving as the proportionality constant.

3. Importance of Cubical Edge Length Calculation

Details: Calculating the cubical edge length is essential for understanding the geometric properties of the Tetrakis Hexahedron, including its volume, surface area, and other dimensional relationships. This measurement is particularly important in crystallography, materials science, and architectural design applications.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will automatically compute the corresponding cubical edge length using the mathematical relationship between these two parameters.

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 added to each face. 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. For the Tetrakis Hexahedron, this sphere touches every edge at exactly one point.

Q3: Why is the square root of 2 used in this formula?
A: The square root of 2 appears due to the geometric relationships within the Tetrakis Hexahedron structure, specifically the 45-degree angles formed between certain edges and the midsphere tangency points.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different mathematical relationships between their midsphere radii and edge lengths.

Q5: What are practical applications of this calculation?
A: This calculation is used in various fields including crystallography for determining crystal structures, in materials science for nanoparticle design, and in architecture for creating complex geometric structures.