1. What Is The Long Edge Of Pentagonal Icositetrahedron?

The Long Edge of Pentagonal Icositetrahedron is the length of the longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Icositetrahedron. It is a geometric property of this particular polyhedron.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( [Tribonacci_C] \) — Tribonacci constant (1.839286755214161)
• \( Snub\ Cube\ Edge \) — Length of any edge of the Snub Cube

Explanation: This formula calculates the long edge length based on the snub cube edge length and the mathematical constant Tribonacci_C.

3. Importance Of Calculation

Details: Accurate calculation of geometric properties is crucial for mathematical modeling, 3D design, architectural applications, and understanding the structural properties of polyhedra.

4. Using The Calculator

Tips: Enter the snub cube edge length in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a polyhedron with 24 pentagonal faces. It is the dual of the snub cube.

Q2: What is the Tribonacci constant?
A: The Tribonacci constant is the real root of the equation x³ - x² - x - 1 = 0, approximately equal to 1.839286755214161.

Q3: How is this formula derived?
A: The formula is derived from the geometric relationships between the snub cube and its dual, the pentagonal icositetrahedron.

Q4: What are the applications of this calculation?
A: This calculation is used in geometry, crystallography, architectural design, and mathematical research involving polyhedra.

Q5: Are there any limitations to this formula?
A: The formula is specifically designed for the pentagonal icositetrahedron and may not apply to other polyhedra or geometric shapes.