1. What is NonSymmetry Diagonal of Deltoidal Hexecontahedron?

The NonSymmetry Diagonal of Deltoidal Hexecontahedron is the length of the diagonal which divides the deltoid faces of Deltoidal Hexecontahedron into two isosceles triangles. It is an important geometric property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( d_{Non\ Symmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)
• \( r_i \) — Insphere Radius of Deltoidal Hexecontahedron (m)
• \( \sqrt{5} \) — Mathematical constant (approximately 2.23607)

3. Formula Explanation

Details: This formula derives from the geometric properties of the Deltoidal Hexecontahedron, relating the non-symmetry diagonal to the insphere radius through mathematical constants and relationships specific to this polyhedron.

4. Using the Calculator

Tips: Enter the insphere radius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding non-symmetry diagonal length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a Catalan solid with 60 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 be inscribed within the polyhedron, touching all faces.

Q3: Why is this diagonal called "non-symmetry"?
A: It's called non-symmetry diagonal because it divides the deltoid faces asymmetrically into two isosceles triangles.

Q4: What are the units of measurement?
A: Both input (insphere radius) and output (non-symmetry diagonal) are in meters, but any consistent length unit can be used.

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