1. What is Long Edge of Deltoidal Hexecontahedron?

The Long Edge of Deltoidal Hexecontahedron is the length of the longest edge of the identical deltoidal faces of a Deltoidal Hexecontahedron. This polyhedron has 60 deltoidal faces and is a Catalan solid.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• Midsphere Radius — The radius of the sphere tangent to all edges of the Deltoidal Hexecontahedron
• √5 — Square root of 5 (approximately 2.23607)

3. Mathematical Formula Explanation

Details: This formula establishes the relationship between the midsphere radius and the long edge length of a Deltoidal Hexecontahedron. The constant factors (20, 3, 5, and 3) along with √5 are derived from the geometric properties of this specific polyhedron.

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 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 deltoidal (kite-shaped) faces, 120 edges, and 62 vertices.

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: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Deltoidal Hexecontahedron.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Deltoidal Hexecontahedron.

Q5: What are typical values for the midsphere radius?
A: The midsphere radius depends on the specific size of the polyhedron, but it must be a positive real number.