Formula Used:
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The Icosahedral Edge Length of Triakis Icosahedron refers to the length of the edges that form the underlying icosahedral structure of a Triakis Icosahedron. It is a fundamental geometric measurement in this polyhedral shape.
The calculator uses the formula:
Where:
Explanation: This formula calculates the icosahedral edge length based on the insphere radius, using the mathematical relationship derived from the geometry of the Triakis Icosahedron.
Details: Calculating the icosahedral edge length is essential for understanding the geometric properties, spatial dimensions, and structural characteristics of Triakis Icosahedrons in mathematical and engineering applications.
Tips: Enter the insphere radius in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron, featuring 60 isosceles triangular faces.
Q2: How is the insphere radius defined?
A: The insphere radius is the radius of the largest sphere that can be contained within the Triakis Icosahedron, touching all its faces.
Q3: What are typical applications of this calculation?
A: This calculation is used in geometry research, architectural design, molecular modeling, and various engineering applications involving polyhedral structures.
Q4: Are there limitations to this formula?
A: This formula is specifically derived for Triakis Icosahedrons and may not apply to other polyhedral shapes or irregular geometries.
Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, suitable for most mathematical and engineering applications.