1. What is Long Edge of Deltoidal Hexecontahedron?

The Long Edge of Deltoidal Hexecontahedron is the length of longest edge of the identical deltoidal faces of Deltoidal Hexecontahedron. It is an important geometric measurement in this polyhedron structure.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( ri \) — Insphere Radius of Deltoidal Hexecontahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the long edge length based on the insphere radius using mathematical constants and geometric relationships specific to the deltoidal hexecontahedron.

3. Importance of Long Edge Calculation

Details: Calculating the long edge is crucial for understanding the geometric properties of deltoidal hexecontahedron, including surface area, volume, and other dimensional relationships in this complex polyhedral structure.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding long edge length of the deltoidal hexecontahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a deltoidal hexecontahedron?
A: A deltoidal hexecontahedron is a Catalan solid with 60 congruent deltoid faces, 120 edges, and 62 vertices.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can fit inside the polyhedron, touching all faces tangentially.

Q3: Are there other edges in deltoidal hexecontahedron?
A: Yes, the deltoidal hexecontahedron has both long and short edges due to its deltoidal face shape.

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

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect deltoidal hexecontahedrons and provides precise calculations based on the given insphere radius.