Short Edge Of Pentagonal Icositetrahedron Given Insphere Radius Calculator

Formula Used:

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

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 polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Short Edge} = 2 \times \sqrt{\frac{(2 - C) \times (3 - C)}{C + 1}} \times r_i \]

Where:

\( C \) — Tribonacci constant (≈1.839286755214161)
\( r_i \) — Insphere radius of the Pentagonal Icositetrahedron

Explanation: This formula relates the short edge length to the insphere radius through mathematical constants and geometric relationships specific to the Pentagonal Icositetrahedron structure.

3. Importance of Short Edge Calculation

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

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 short edge length using the mathematical relationship derived from the geometry of Pentagonal Icositetrahedrons.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a polyhedron with 24 pentagonal faces. It is one of the Catalan solids and 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, approximately equal to 1.839286755214161. It appears in various mathematical contexts including this geometric formula.

Q3: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can be inscribed within the Pentagonal Icositetrahedron, touching all its faces.

Q4: Are there other edges in a Pentagonal Icositetrahedron?
A: Yes, besides the short edge, Pentagonal Icositetrahedrons also have medium and long edges, each with different geometric relationships and formulas.

Q5: What are typical applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, crystallography studies, and mathematical research involving polyhedral structures and their properties.