Jump to content

File:Twisted square antiprism.png

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (1,000 × 957 pixels, file size: 238 KB, MIME type: image/png)

Summary

Description
English: This solid can be called a twisted square prism because it can be formed by "twisting" a square prism.

But there are two ways one can "twist" a square prism (or rectangular prism):

  • If I physically twist a clay prism, the four connecting squares (or rectangles) become twisted parallelograms (not the solid shown).
  • If I rotate the top square relative to the bottom square, and only allow straight edges and planar faces, nothing "slips" or "snaps" (like with the gyrobicupolae). I must replace the four connecting squares (or rectangles) with four pairs of triangles (as shown here). That operation seems like more than just "twisting". Also, the resulting "twisted prism is topologically identical to the antiprism" – a prism becomes an antiprism for any twist other than 0 degrees.

If I rotate the top square relative to the bottom square of a uniform [or regular] square antiprism, the triangles change proportions, but the number of faces does not change.

"Twisted square antiprism" names this solid unambiguously, and is in use for it (Twisted antiprism on Wolfram), so it seems preferable.
Date
Source Own work
Author Tomruen
Other versions
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “Twisted square antiprism.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

inception

2 March 2015

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current08:59, 2 March 2015Thumbnail for version as of 08:59, 2 March 20151,000 × 957 (238 KB)TomruenUser created page with UploadWizard

The following 2 pages use this file:

Global file usage

The following other wikis use this file:

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Retrieved from "https://en.wikipedia.org/wiki/File:Twisted_square_antiprism.png"