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 (m)
• \( r_m \) — Midsphere Radius (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the insphere radius of a deltoidal icositetrahedron based on its given midsphere radius, using mathematical constants derived from the geometric properties of this specific polyhedron.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and 3D modeling as it helps determine the maximum size of a sphere that can be inscribed within the polyhedron, which has applications in packaging, material science, and architectural design.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding insphere radius using the mathematical relationship between these two properties of the deltoidal icositetrahedron.

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. It is the dual polyhedron of the rhombicuboctahedron.

Q2: What's the difference between insphere radius and midsphere radius?
A: The insphere radius is the radius of the largest sphere that fits inside the polyhedron, while the midsphere radius is the radius of the sphere that touches all the edges of the polyhedron.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the deltoidal icositetrahedron. Other polyhedra have different mathematical relationships between their insphere and midsphere radii.

Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, architectural design, and any field that involves working with this specific polyhedral shape.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect deltoidal icositetrahedron. The accuracy depends on the precision of the input value and the implementation of the mathematical operations.