Total Surface Area Of Disheptahedron Given Circumsphere Radius Calculator

Formula Used:

\[ TSA = 2 \times (3 + \sqrt{3}) \times r_c^2 \]

Total Surface Area of Disheptahedron:

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1. What is the Total Surface Area of Disheptahedron?

The Total Surface Area of a Disheptahedron is the total amount of two-dimensional space occupied by all the faces of the Disheptahedron. It's an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times (3 + \sqrt{3}) \times r_c^2 \]

Where:

\( TSA \) — Total Surface Area of Disheptahedron (m²)
\( r_c \) — Circumsphere Radius of Disheptahedron (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula calculates the total surface area based on the circumsphere radius, which is the radius of the sphere that contains the Disheptahedron with all vertices touching the sphere.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, structural analysis, and geometric modeling of this complex polyhedron.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. 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 Circumsphere Radius?
A: The circumsphere radius is the radius of the sphere that contains the polyhedron such that all vertices of the polyhedron are touching the sphere.

Q3: How accurate is this formula?
A: The formula is mathematically exact for a perfect Disheptahedron with the given circumsphere radius.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula applies only to the Disheptahedron. Other polyhedra have different surface area formulas.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in geometry research, architectural design, 3D modeling, and materials science where precise surface area measurements are needed.