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The Icosahedral Edge Length of Triakis Icosahedron refers to the length of the edges of the underlying icosahedron in a Triakis Icosahedron, which is a polyhedron created by attaching a triangular pyramid to each face of a regular icosahedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the edge length of the underlying icosahedron based on the total surface area of the Triakis Icosahedron, using mathematical constants and geometric relationships.
Details: Calculating the icosahedral edge length is important for understanding the geometric properties of Triakis Icosahedron, including its volume, surface area relationships, and structural characteristics in various applications.
Tips: Enter the total surface area of the Triakis Icosahedron in square 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 created by attaching a triangular pyramid to each face of a regular icosahedron, resulting in a polyhedron with 60 faces.
Q2: How is this formula derived?
A: The formula is derived from geometric relationships between the total surface area and the edge length of the underlying icosahedron in a Triakis Icosahedron.
Q3: What are the units for the input and output?
A: The input (total surface area) should be in square meters (m²), and the output (edge length) will be in meters (m).
Q4: Can this calculator handle very large or very small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by PHP's floating-point precision.
Q5: What are some practical applications of this calculation?
A: This calculation is useful in geometry, crystallography, architecture, and various fields where polyhedral structures are studied or utilized.