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. This sphere is tangent to all the deltoidal faces of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius of Deltoidal Icositetrahedron (m)
• \( l_e(Short) \) — Short Edge of Deltoidal Icositetrahedron (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the radius of the largest sphere that can fit inside the Deltoidal Icositetrahedron, tangent to all its faces, based on the length of its shortest edge.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and materials science for understanding the spatial properties of polyhedra, packing efficiency, and in applications involving spherical inclusions within crystalline structures.

4. Using the Calculator

Tips: Enter the Short Edge length 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 identical deltoidal faces. It is the dual polyhedron of the rhombicuboctahedron.

Q2: How is the insphere radius different from circumsphere radius?
A: The insphere radius is the radius of the sphere inside the polyhedron that touches all faces, while the circumsphere radius is the radius of the sphere that contains the polyhedron with all vertices on the sphere.

Q3: What are the practical applications of this calculation?
A: This calculation is used in crystallography, materials science, architecture, and 3D modeling where precise geometric properties of polyhedra are required.

Q4: 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 their insphere radii.

Q5: What units should be used for the input?
A: The calculator uses meters as the default unit, but any consistent unit system can be used as long as the same unit is maintained throughout the calculation.