- 1. What is the dual polyhedron of the pentagonal trapezohedron?
A) Pentagonal antiprism
B) Regular dodecahedron
C) Cube
D) Pentagonal pyramid
- 2. How many faces does a pentagonal trapezohedron have?
A) Twenty
B) Ten
C) Twelve
D) Five
- 3. What is the shape of the faces of a pentagonal trapezohedron?
A) Triangles
B) Squares
C) Kites
D) Pentagons
- 4. How many vertices does a pentagonal trapezohedron have?
A) Ten
B) Twenty
C) Twelve
D) Five
- 5. How many edges does a pentagonal trapezohedron have?
A) Twelve
B) Thirty
C) Ten
D) Twenty
- 6. What symmetry group does the pentagonal trapezohedron share with the pentagonal antiprism?
A) Td
B) D5d
C) D5h
D) Oh
- 7. What is the order of the symmetry group D5d?
A) 30
B) 10
C) 20
D) 12
- 8. When was the pentagonal trapezohedron first patented as a gaming die?
A) 1980
B) 1900
C) 1920
D) 1906
- 9. When considering a version with all vertices on the surface of a sphere, what are two of the internal angles of the kite faces?
A) 108 degrees
B) 45 degrees
C) 90 degrees
D) 36 degrees
- 10. What happens if you truncate the top and bottom vertices of a pentagonal trapezohedron?
A) It becomes a cube
B) It achieves a regular dodecahedron
C) It becomes a pentagonal pyramid
D) It becomes a pentagonal antiprism
- 11. In the standard kite face of a pentagonal trapezohedron, what are the internal angles?
A) 90 degrees and 45 degrees
B) 108 degrees and 36 degrees
C) 72 degrees and 108 degrees
D) 60 degrees and 120 degrees
- 12. Why are some ten-sided dice sold in sets where one is numbered 00 to 90?
A) To increase weight
B) To create a 100-sided effect
C) To distinguish between tens and units
D) To prevent cheating
- 13. What is the position of the vertices in the spherical tiling of the pentagonal trapezohedron?
A) All on the poles
B) 2 on the poles and alternating on the equator
C) Randomly distributed
D) All on the equator
- 14. Which event saw a patent refinement of the ten-sided die become notorious?
A) The 1975 Gaming Convention
B) 1906 World Fair
C) 1980 Gen Con
D) 1990 Game Expo
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