Formula Used:
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The Total Surface Area of an Icosidodecahedron is the total quantity of plane enclosed by the entire surface of this Archimedean solid. It represents the sum of the areas of all its faces, which include both triangular and pentagonal faces.
The calculator uses the formula:
Where:
Explanation: This formula calculates the total surface area based on the circumsphere radius, incorporating mathematical constants and square root functions specific to the geometry of the icosidodecahedron.
Details: Calculating the surface area of geometric solids like the icosidodecahedron is important in various fields including mathematics, architecture, materials science, and 3D modeling. It helps in understanding the geometric properties and spatial characteristics of these complex shapes.
Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the total surface area using the mathematical formula.
Q1: What is an Icosidodecahedron?
A: An icosidodecahedron is an Archimedean solid with 32 faces - 20 triangles and 12 pentagons, 30 vertices, and 60 edges.
Q2: What is the Circumsphere Radius?
A: The circumsphere radius is the radius of the sphere that contains the icosidodecahedron such that all vertices lie on the sphere's surface.
Q3: Are there other ways to calculate surface area?
A: Yes, surface area can also be calculated using edge length or midsphere radius, but this calculator uses the circumsphere radius as input.
Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, molecular modeling, game development, and mathematical research involving polyhedral geometry.
Q5: How accurate is the calculation?
A: The calculation is mathematically exact, though the displayed result is rounded to 6 decimal places for practical purposes.