1. What is 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)
• \( d_{Symmetry} \) — Symmetry Diagonal of Deltoidal Icositetrahedron (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the insphere radius based on the symmetry diagonal of the deltoidal icositetrahedron, using mathematical constants derived from the geometry of this specific polyhedron.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and materials science for understanding the packing properties, volume relationships, and spatial characteristics of the deltoidal icositetrahedron shape.

4. Using the Calculator

Tips: Enter the symmetry diagonal of the deltoidal icositetrahedron in 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 Symmetry Diagonal?
A: The Symmetry Diagonal is the diagonal that cuts the deltoid faces of Deltoidal Icositetrahedron into two equal halves.

Q3: What are typical values for the Insphere Radius?
A: The insphere radius depends on the size of the polyhedron. For a deltoidal icositetrahedron with symmetry diagonal of 1 meter, the insphere radius is approximately 0.65 meters.

Q4: What are the applications of this calculation?
A: This calculation is used in crystallography, architectural design, and geometric modeling where deltoidal icositetrahedron shapes occur.

Q5: How accurate is this formula?
A: The formula is mathematically exact for the ideal deltoidal icositetrahedron shape and provides precise results when correct inputs are used.