1. What is Midsphere Radius of Deltoidal Icositetrahedron?

The Midsphere Radius of Deltoidal Icositetrahedron is the radius of the sphere that is tangent to all edges of the Deltoidal Icositetrahedron. This polyhedron is a Catalan solid with 24 deltoid faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere radius (m)
• \( V \) — Volume of Deltoidal Icositetrahedron (m³)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the midsphere radius from the volume of the deltoidal icositetrahedron, using the mathematical relationship between these geometric properties.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and crystallography for understanding the spatial properties and symmetry of this particular polyhedron.

4. Using the Calculator

Tips: Enter the volume of the deltoidal icositetrahedron in cubic meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoid (kite-shaped) faces, 26 vertices, and 48 edges.

Q2: What is the significance of the midsphere?
A: The midsphere is the sphere that is tangent to all edges of a polyhedron, providing important geometric information about the shape.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the deltoidal icositetrahedron. Other polyhedra have different formulas for calculating midsphere radius.

Q4: What units should be used for volume input?
A: The calculator expects volume input in cubic meters (m³), and returns the midsphere radius in meters (m).

Q5: How accurate is the calculation?
A: The calculation is mathematically exact based on the given formula. The result is rounded to 6 decimal places for practical use.