1. What is Midsphere Radius of Tetrakis Hexahedron?

The Midsphere Radius of Tetrakis Hexahedron is the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere. It represents the sphere that touches all the edges of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius (m)
• \( l_{e(Cube)} \) — Cubical Edge Length (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the midsphere radius by dividing the cubical edge length by the square root of 2.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling as it helps understand the spatial properties and relationships of the Tetrakis Hexahedron polyhedron.

4. Using the Calculator

Tips: Enter the cubical edge length 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 a square pyramid on each face.

Q2: What is the relationship between cubical edge length and midsphere radius?
A: The midsphere radius is equal to the cubical edge length divided by the square root of 2.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first.

Q4: What is the significance of the midsphere in polyhedral geometry?
A: The midsphere (or intersphere) is significant as it touches all the edges of the polyhedron, providing important geometric properties.

Q5: Are there other ways to calculate the midsphere radius?
A: For Tetrakis Hexahedron, this is the standard formula. Other polyhedra may have different formulas for calculating their midsphere radii.