1. What is Long Edge of Deltoidal Icositetrahedron?

The Long Edge of Deltoidal Icositetrahedron is the length of the longest edge of the identical deltoidal faces that make up this polyhedron. It is an important geometric measurement in understanding the structure and properties of this specific shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Midsphere Radius — The radius of the sphere tangent to all edges of the Deltoidal Icositetrahedron
• \(\sqrt{2}\) — Square root of 2 (approximately 1.4142)

Explanation: This formula establishes a direct mathematical relationship between the midsphere radius and the long edge length of the deltoidal icositetrahedron.

3. Importance of Long Edge Calculation

Details: Calculating the long edge is crucial for geometric analysis, architectural applications, and understanding the spatial properties of this specific polyhedron. It helps in determining proportions and scaling factors for various practical applications.

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 long edge length.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Are there other ways to calculate the long edge?
A: Yes, the long edge can also be calculated using other geometric properties such as volume, surface area, or short edge length.

Q4: What are typical applications of this calculation?
A: This calculation is used in geometry research, architectural design, crystal structure analysis, and mathematical modeling.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the deltoidal icositetrahedron.