Long Edge of Deltoidal Hexecontahedron Given Nonsymmetry Diagonal Calculator

Formula Used:

\[ le_{Long} = \frac{11 \times d_{Non\ Symmetry}}{\sqrt{\frac{470 + 156\sqrt{5}}{5}}} \]

Long Edge of Deltoidal Hexecontahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the 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 specific polyhedron structure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ le_{Long} = \frac{11 \times d_{Non\ Symmetry}}{\sqrt{\frac{470 + 156\sqrt{5}}{5}}} \]

Where:

\( le_{Long} \) — Long Edge of Deltoidal Hexecontahedron (m)
\( d_{Non\ Symmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)

Explanation: This formula establishes a precise mathematical relationship between the non-symmetry diagonal and the long edge of the deltoidal hexecontahedron, incorporating the golden ratio constant through the √5 term.

3. Importance of Long Edge Calculation

Details: Calculating the long edge is crucial for geometric analysis, architectural applications, and mathematical modeling involving deltoidal hexecontahedrons. It helps in understanding the spatial properties and proportions of this complex polyhedron.

4. Using the Calculator

Tips: Enter the NonSymmetry Diagonal value in meters. The value must be positive and non-zero. The calculator will automatically compute the corresponding Long Edge measurement.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A deltoidal hexecontahedron is a Catalan solid with 60 deltoid faces, 62 vertices, and 120 edges. It is the dual polyhedron of the rhombicosidodecahedron.

Q2: How is the NonSymmetry Diagonal defined?
A: The NonSymmetry Diagonal of Deltoidal Hexecontahedron is the length of the diagonal which divides the deltoid faces into two isosceles triangles.

Q3: What are the practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, mathematical research, and geometric modeling where precise polyhedral measurements are required.

Q4: Why does the formula contain √5?
A: The √5 term appears because the deltoidal hexecontahedron's geometry is related to the golden ratio, which is fundamental to many polyhedral structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the deltoidal hexecontahedron, providing precise results for any valid input value.