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The Surface to Volume Ratio (SA:V) of a Small Stellated Dodecahedron is the numerical ratio of the total surface area to the volume of this polyhedron. It's an important geometric property that describes how much surface area is available per unit volume.
The calculator uses the mathematical formula:
Where:
Explanation: The formula calculates the surface to volume ratio based on the circumradius of the polyhedron, incorporating mathematical constants and geometric relationships specific to the Small Stellated Dodecahedron.
Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. It helps understand properties like reactivity, heat transfer, and diffusion rates in geometric structures.
Tips: Enter the circumradius value in meters. The value must be positive and non-zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).
Q1: What is a Small Stellated Dodecahedron?
A: It's a Kepler-Poinsot polyhedron that consists of 12 pentagram faces with five pentagrams meeting at each vertex.
Q2: Why is surface to volume ratio important?
A: It indicates how much surface area is available relative to the volume, which affects properties like chemical reactivity and heat dissipation.
Q3: What units are used for the calculation?
A: Circumradius is in meters (m) and the resulting ratio is in reciprocal meters (m⁻¹).
Q4: Can this calculator handle very small or large values?
A: Yes, as long as the input values are positive and within reasonable computational limits.
Q5: Is this formula specific to the Small Stellated Dodecahedron?
A: Yes, this formula is derived specifically for the geometric properties of the Small Stellated Dodecahedron.