Short Edge Of Pentagonal Icositetrahedron Given Surface To Volume Ratio Calculator

Formula Used:

\[ \text{Short Edge} = \frac{3\sqrt{\frac{22(5[Tribonacci_C]-1)}{(4[Tribonacci_C])-3}}}{(SA:V \times \sqrt{\frac{11([Tribonacci_C]-4)}{2((20[Tribonacci_C])-37)}}) \times \sqrt{[Tribonacci_C]+1}} \]

Short Edge of Pentagonal Icositetrahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Short Edge of Pentagonal Icositetrahedron?

The Short Edge of Pentagonal Icositetrahedron is the length of the shortest edge which forms the base and middle edge of the axial-symmetric pentagonal faces of a Pentagonal Icositetrahedron. It is a key geometric parameter in this complex polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the specialized formula:

\[ \text{Short Edge} = \frac{3\sqrt{\frac{22(5[Tribonacci_C]-1)}{(4[Tribonacci_C])-3}}}{(SA:V \times \sqrt{\frac{11([Tribonacci_C]-4)}{2((20[Tribonacci_C])-37)}}) \times \sqrt{[Tribonacci_C]+1}} \]

Where:

\( [Tribonacci_C] \) — Tribonacci constant (≈1.839286755214161)
\( SA:V \) — Surface to Volume Ratio of Pentagonal Icositetrahedron (1/m)

Explanation: This formula relates the short edge length to the surface-to-volume ratio using the mathematical constant Tribonacci_C, which appears in various geometric and fractal patterns.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is essential for understanding the geometric properties, symmetry, and spatial characteristics of Pentagonal Icositetrahedrons, which have applications in crystallography, architecture, and mathematical modeling.

4. Using the Calculator

Tips: Enter the Surface to Volume Ratio (SA:V) in units of 1/meter. The value must be positive and valid for accurate calculation of the short edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a 24-faced polyhedron where each face is an irregular pentagon, exhibiting complex symmetry patterns.

Q2: What is the Tribonacci constant?
A: The Tribonacci constant is the real root of the equation x³ = x² + x + 1, approximately equal to 1.839286755214161, appearing in various mathematical contexts.

Q3: How is Surface to Volume Ratio measured?
A: Surface to Volume Ratio is calculated as the total surface area divided by the total volume of the polyhedron, typically expressed in units of 1/length.

Q4: What are typical values for SA:V ratio?
A: The SA:V ratio depends on the specific dimensions of the polyhedron, but generally ranges based on the scale and proportions of the geometric shape.

Q5: Can this calculator be used for other polyhedra?
A: No, this specific formula applies only to Pentagonal Icositetrahedrons due to their unique geometric properties and the involvement of the Tribonacci constant.