Midsphere Radius of Disheptahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ r_m = \frac{3\sqrt{3}(3+\sqrt{3})}{5\sqrt{2} \times \frac{A}{V}} \]

Midsphere Radius (rₘ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Midsphere Radius of Disheptahedron?

The Midsphere Radius of Disheptahedron is the radius of the sphere for which all the edges of the Disheptahedron become a tangent line to that sphere. It represents the sphere that touches all the edges of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{3\sqrt{3}(3+\sqrt{3})}{5\sqrt{2} \times \frac{A}{V}} \]

Where:

\( r_m \) — Midsphere Radius (m)
\( \frac{A}{V} \) — Surface to Volume Ratio (1/m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula calculates the midsphere radius based on the surface to volume ratio of the disheptahedron, using mathematical constants and geometric relationships.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometric modeling and 3D design applications. It helps in understanding the spatial properties and proportions of the disheptahedron shape.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Disheptahedron?
A: A Disheptahedron is a polyhedron with fourteen faces, typically combining triangular and square faces in a specific geometric arrangement.

Q2: What is the significance of the midsphere?
A: The midsphere (or midsphere) is the sphere that is tangent to all edges of a polyhedron, providing important geometric information about the shape's proportions.

Q3: How is surface to volume ratio measured?
A: Surface to volume ratio is calculated by dividing the total surface area by the volume of the polyhedron, typically measured in square meters per cubic meter (1/m).

Q4: What are typical values for midsphere radius?
A: The midsphere radius varies depending on the specific dimensions of the disheptahedron, but is typically in the range of centimeters to meters for practical applications.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the disheptahedron geometry. Other polyhedra have different formulas for calculating their midsphere radii.