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The volume of a Triakis Icosahedron is the amount of three-dimensional space enclosed by its surface. It is a Catalan solid that can be derived from the icosahedron by adding pyramids to each face.
The calculator uses the formula:
Where:
Explanation: The formula calculates the volume based on the pyramidal edge length, incorporating the mathematical constant √5 which is characteristic of icosahedral geometry.
Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, and architecture. For the Triakis Icosahedron, understanding its volume helps in material estimation, structural analysis, and spatial planning applications.
Tips: Enter the pyramidal edge length in meters. The value must be positive and non-zero. The calculator will compute the volume using the precise mathematical formula.
Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that results from adding a triangular pyramid to each face of a regular icosahedron, creating a polyhedron with 60 faces.
Q2: Why does the formula contain √5?
A: The √5 appears because it's intrinsically related to the geometry of regular icosahedra and their derivatives, representing the golden ratio relationship in their structure.
Q3: What are the units of measurement?
A: The pyramidal edge length should be in meters, and the resulting volume will be in cubic meters (m³). You can convert from other units as needed.
Q4: Can this calculator handle very large or small values?
A: Yes, the calculator can process a wide range of positive values, though extremely large or small numbers may be limited by PHP's floating-point precision.
Q5: Is this formula exact or approximate?
A: The formula is mathematically exact. The calculator provides a numerical approximation based on the input value, with results rounded to 6 decimal places for clarity.