Hexa-Twistor Triangular Section
Year: 2003 Authors: Akio Hizume
Core claim
A Hexa-Twistor triangular section can be constructed as a precise paper model from repeated units, and the author suggests scaling the method to public or play sculpture.
Topics
twisted surface geometry, paper modeling, developable surfaces, sculptural fabrication
Domains
geometric surfaces, developable geometry, poly-twistor forms, paper craft, public sculpture, play sculpture, visual form
Methods
VRML visualization, paper assembly, surface development, modular construction
Media
Paper text
The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.
ISAMA The International Society of the Arts, Mathematics, and Architecture BRIDGES Mathematical Connections in Art, Music, and Science
Hexa-Twistor Triangular Section
Akio Hizume Star Cage Institute of Geometry Arachi 1793-14, Ichinomiya, Chosei, Chiba, JAPAN E-mail: starcage@mbb.nifty.com http://homepage1.nifty.com/starcage/
Figure 1: VRML image
The Hexa-Twistor [1] is one category of the Poly-Twistor [2]. Fig. 1 is an example of the Hexa-Twistor produced by VRML. It consists of six helical-tori whose sections are constant regular triangle [3]. Therefore it consists of developable surfaces.
I actually made a model of the Hexa-Twistor using paper [4]. The unit is made of three developments but the shapes are only two kinds as shown in Fig. 2. Five units make one helical-torus. Six helical-tori make one Hexa-Twistor (Fig.3, 4).
It was ultrasophisticated work. It does not allow any error. The surface is very whipcord. It produces full of shades and shadows.
I can make actual models of any type of Poly-Twistor in the same way. I would like to build big one as public sculpture or play sculpture.
Figure 2: Developments and an assembled unit.
Figure 3: An assembled helica- torus.
Figure 4: An assembled Hexa-Twistor.
References
[1] Akio Hizume Hexa-Twistor, MANIFOLD #01, pp. 10-12, 2000. (Japanese paper) [2] Akio Hizume Poly-Twistor, Japanese thesis were published on MANIFOLD #04, pp. 8-9, 2002. The English thesis was published at the ISAMA, 2002 Freiburg. [3] Akio Hizume Hexa-Twistor Triangular Section, MANIFOLD, #05, pp. 10, 2002. [4] This paper is brief translation of Japanese paper, that is, Akio Hizume, An actual model of Hexa-Twistor Triangular Section, MANIFOLD, #06, pp. 7-8 2003.