Can anyone tell me the real names of these 3D shapes?

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Discussion Overview

The discussion revolves around identifying the names of various 3D shapes, specifically focusing on the terms "cuboid" and "rectangular prism." Participants explore the definitions and distinctions between these terms, as well as the implications of using historical nomenclature in geometry.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants identify the second last shape as a cuboid and the last shape as a triangular prism.
  • Others argue that "cuboid" is ambiguous and that "rectangular prism" is a more specific term for a 3D shape with rectangular cross-sections.
  • One participant points out that historical names for shapes should be respected, comparing it to how a square is defined.
  • Another participant references a definition from a wiki source, noting that mathematical literature may use "cuboid" more broadly than some other sources.
  • Questions are raised about whether the original diagram specifies right angles or square faces, which could affect the classification of the shapes.
  • Some participants express that the shapes in the original post do not match their understanding of cuboids, suggesting a potential discrepancy in visual representation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions of "cuboid" and "rectangular prism," with multiple competing views remaining regarding the appropriateness of these terms and their implications in geometry.

Contextual Notes

The discussion highlights the ambiguity in the term "cuboid" and its usage in different contexts, as well as the lack of specification in the original diagram regarding angles and face shapes.

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I know cylinder, cone and cube, but can't think of the names for the last two. I know this is a very basic question that I should know...but I am blanking. View attachment 6204
 

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The last two are prisms, a rectangular prism and a right triangular prism.
 
Second last one is precisely known as cuboid and the last one is a triangular prism (as MarkFL said).
 
phymat said:
Second last one is precisely known as cuboid and the last one is a triangular prism (as MarkFL said).

I don't think there's anything precise with the term "cuboid" as it simply means "cube-like". "Rectangular Prism" is much more specific, as being a 3D shape with all identical rectangular cross-sections...
 
Prove It said:
I don't think there's anything precise with the term "cuboid" as it simply means "cube-like". "Rectangular Prism" is much more specific, as being a 3D shape with all identical rectangular cross-sections...

If a name has been given to a 3D shape by ancient mathematicians, why not use it? A square will be called a square, not a rectangle with all sides equal. :)
 
phymat said:
If a name has been given to a 3D shape by ancient mathematicians, why not use it? A square will be called a square, not a rectangle with all sides equal. :)

From wiki:
In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While mathematical literature refers to any such polyhedron as a cuboid,[1] other sources use "cuboid" to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle); this more restrictive type of cuboid is also known as a rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.[2]


So for starters "cuboid" is somewhat ambiguous, and more specifically mathematical literature refers to it without requiring right angles or square faces, while cube and right rectangular prism are well-defined with square respectively rectangular faces.
 
phymat said:
If a name has been given to a 3D shape by ancient mathematicians, why not use it? A square will be called a square, not a rectangle with all sides equal. :)

Ancient mathematicians also believed that all numbers were rational and killed anyone who could prove otherwise. Yes, why not use their logic?
 
I like Serena said:
From wiki:
In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While mathematical literature refers to any such polyhedron as a cuboid,[1] other sources use "cuboid" to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle); this more restrictive type of cuboid is also known as a rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.[2]


So for starters "cuboid" is somewhat ambiguous, and more specifically mathematical literature refers to it without requiring right angles or square faces, while cube and right rectangular prism are well-defined with square respectively rectangular faces.


Does the diagram posted by OP specify right angles or square faces?
Also, how would you define a cuboid?
 
phymat said:
Does the diagram posted by OP specify right angles or square faces?
Also, how would you define a cuboid?

Examples of cuboids... I think they look different from what is shown in the OP...

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  • #10
I like Serena said:
Examples of cuboids... I think they look different from what is shown in the OP...

They 'look' different, but it is nowhere specified in the original diagram by OP that all angles are right angles and 4 faces are rectangular. Since it is not specified, cuboid is the most appropriate name for the shape. In a case that it had been specified, it could have been called as rectangular cuboid.
 

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