Snub Cube Edge of Pentagonal Icositetrahedron given Midsphere Radius Calculator

Formula Used:

\[ \text{Snub Cube Edge of Pentagonal Icositetrahedron} = 2 \times \sqrt{2 - [Tribonacci_C]} \times \text{Midsphere Radius of Pentagonal Icositetrahedron} \]

Snub Cube Edge of Pentagonal Icositetrahedron:

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1. What is Snub Cube Edge of Pentagonal Icositetrahedron?

The Snub Cube Edge of Pentagonal Icositetrahedron is the length of any edge of the Snub Cube of which dual body is the Pentagonal Icositetrahedron. It represents a fundamental geometric measurement in polyhedral mathematics.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ \text{Snub Cube Edge} = 2 \times \sqrt{2 - [Tribonacci_C]} \times \text{Midsphere Radius} \]

Where:

\( [Tribonacci_C] \) — Tribonacci constant (≈1.839286755214161)
Midsphere Radius — Radius of the midsphere of Pentagonal Icositetrahedron (m)

Explanation: This formula establishes the relationship between the snub cube edge length and the midsphere radius using the mathematical constant Tribonacci_C.

3. Importance of Snub Cube Edge Calculation

Details: Calculating the snub cube edge length is essential in geometric modeling, crystallography, and mathematical studies of polyhedral structures. It helps in understanding the spatial relationships and properties of complex geometric shapes.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding snub cube 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, approximately equal to 1.839286755214161.

Q2: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a Catalan solid with 24 pentagonal faces, serving as the dual polyhedron to the snub cube.

Q3: What is a midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of a polyhedron.

Q4: What are typical applications of this calculation?
A: This calculation is used in mathematical geometry, architectural design, crystallography, and computer graphics modeling.

Q5: How accurate is this formula?
A: The formula is mathematically exact and provides precise results when correct input values are used.