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The Midsphere Radius of an Icosahedron is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere. It's an important geometric property of this regular polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the midsphere radius based on the lateral surface area of the icosahedron, incorporating the golden ratio (φ) which is fundamental to icosahedron geometry.
Details: Calculating the midsphere radius is crucial for understanding the geometric properties of icosahedrons, which have applications in various fields including crystallography, architecture, and molecular modeling.
Tips: Enter the lateral surface area of the icosahedron in square meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is an icosahedron?
A: An icosahedron is a regular polyhedron with 20 equilateral triangular faces, 12 vertices, and 30 edges.
Q2: How is lateral surface area different from total surface area?
A: Lateral surface area excludes the base areas (if any), while total surface area includes all faces. For a regular icosahedron, all faces are identical.
Q3: What are typical applications of icosahedrons?
A: Icosahedrons are used in geodesic domes, viral capsid structures, and various mathematical and geometric studies.
Q4: Why does the formula include the golden ratio?
A: The golden ratio (φ = (1+√5)/2) is intrinsically related to the geometry of regular icosahedrons and appears in many of its dimensional relationships.
Q5: Can this calculator handle different units?
A: The calculator expects input in square meters and outputs in meters. For other units, convert your measurements to meters first.