1. What is the Insphere Radius of Deltoidal Icositetrahedron?

The Insphere Radius of Deltoidal Icositetrahedron is the radius of the sphere that is contained by the Deltoidal Icositetrahedron in such a way that all the faces just touch the sphere. It represents the largest sphere that can fit inside the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius of Deltoidal Icositetrahedron (m)
• \( V \) — Volume of Deltoidal Icositetrahedron (m³)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the insphere radius from the volume of the deltoidal icositetrahedron, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and materials science for understanding the packing properties and spatial relationships within polyhedral structures.

4. Using the Calculator

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

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 are the applications of this calculation?
A: This calculation is used in crystallography, materials science, and geometric modeling where precise spatial relationships are important.

Q3: What units should be used for volume?
A: Volume should be entered in cubic meters (m³) for consistent results with the radius output in meters.

Q4: Are there limitations to this formula?
A: This formula is specifically designed for the deltoidal icositetrahedron and assumes a perfect geometric shape.

Q5: Can this calculator handle very large or small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by PHP's floating-point precision.