Long Edge Of Pentagonal Icositetrahedron Given Insphere Radius Calculator

Formula Used:

\[ \text{Long Edge} = \sqrt{(2 - C) \times (3 - C) \times (C + 1)} \times \text{Insphere Radius} \]

Long Edge Of Pentagonal Icositetrahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Long Edge Of Pentagonal Icositetrahedron?

The Long Edge of Pentagonal Icositetrahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Icositetrahedron. It is an important geometric measurement in this specific polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ \text{Long Edge} = \sqrt{(2 - C) \times (3 - C) \times (C + 1)} \times \text{Insphere Radius} \]

Where:

\( C \) — Tribonacci constant (≈1.839286755214161)
Insphere Radius — Radius of the inscribed sphere (m)

Explanation: This formula relates the long edge length to the insphere radius through the mathematical constant known as the Tribonacci constant, which appears in various geometric and mathematical contexts.

3. Importance of Long Edge Calculation

Details: Calculating the long edge of a pentagonal icositetrahedron is crucial for geometric analysis, architectural design, and mathematical modeling of this specific polyhedral structure. It helps in understanding the spatial properties and proportions of this complex geometric shape.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and non-zero. The calculator will compute the corresponding long edge length using the established mathematical relationship.

5. Frequently Asked Questions (FAQ)

Q1: What is the Tribonacci constant?
A: The Tribonacci constant is a mathematical constant that appears in various geometric and number theory contexts, similar to the Fibonacci constant but for three-term sequences.

Q2: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a polyhedron with 24 pentagonal faces. It's a Catalan solid and the dual of the snub cube.

Q3: 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 its faces.

Q4: Are there practical applications of this calculation?
A: Yes, this calculation is used in crystallography, architectural design, and mathematical modeling of complex geometric structures.

Q5: What units should I use for the input?
A: The calculator uses meters as the unit of measurement, but you can use any consistent unit system as long as you maintain consistency throughout your calculations.