Home Back

Icosahedral Edge Length Of Triakis Icosahedron Given Volume Calculator

Formula Used:

\[ Icosahedral\ Edge\ Length = \sqrt[3]{\frac{44 \times Volume}{5 \times (5 + 7 \times \sqrt{5})}} \]

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is the Icosahedral Edge Length of Triakis Icosahedron?

The Icosahedral Edge Length of Triakis Icosahedron is the length of the line connecting any two adjacent vertices of the icosahedron base of a Triakis Icosahedron. It is a fundamental geometric measurement used in polyhedral geometry and crystallography.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Icosahedral\ Edge\ Length = \sqrt[3]{\frac{44 \times Volume}{5 \times (5 + 7 \times \sqrt{5})}} \]

Where:

Explanation: This formula calculates the edge length of the underlying icosahedron from the volume of the Triakis Icosahedron, using the mathematical relationship between volume and edge length in this specific polyhedral structure.

3. Importance of Icosahedral Edge Length Calculation

Details: Calculating the icosahedral edge length is essential for understanding the geometric properties of Triakis Icosahedrons, which have applications in crystallography, molecular modeling, and architectural design where this specific polyhedral form is utilized.

4. Using the Calculator

Tips: Enter the volume of the Triakis Icosahedron in cubic meters. The volume must be a positive value greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron. It has 60 isosceles triangular faces and is formed by adding triangular pyramids to each face of a regular icosahedron.

Q2: How is this different from a regular Icosahedron?
A: While both are polyhedrons, a regular icosahedron has 20 equilateral triangular faces, whereas a Triakis Icosahedron has 60 isosceles triangular faces and is more complex in structure.

Q3: What are typical applications of this calculation?
A: This calculation is used in crystallography for certain crystal structures, in molecular modeling for specific molecular configurations, and in architectural design for creating complex geometric structures.

Q4: Are there limitations to this formula?
A: This formula assumes a perfect Triakis Icosahedron shape and may not be accurate for irregular or distorted forms of this polyhedron.

Q5: Can this calculator handle different units?
A: The calculator expects volume input in cubic meters. For other units, convert your volume measurement to cubic meters before calculation.

Icosahedral Edge Length Of Triakis Icosahedron Given Volume Calculator© - All Rights Reserved 2025