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Group and Group Isomorphism in Pyraminx

Grup dan Isomorfisma Grup pada Pyraminx

Jurnal Matematika, Statistika dan Komputasi · Vol. 20 No. 2 (2023) · pp. 455–466

DOI
10.20956/j.v20i2.30320
ISSN
2614-8811, 1858-1382
Published
2023-12-24
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

Pyraminx is a twisty puzzle in the shape of a tetrahedron with 4 sides. Pyraminx is played with the bottom completely flat and the front side facing the person holding the Pyraminx. The goal of the Pyraminx game is to randomize the colors, then return the scrambled colors to their original color positions by rotating the sides. This research does not discuss the most effective way of solving Pyraminx but focuses more on proving that movements in Pyraminx form group and that there is a group isomorphism from the group of Pyraminx movements to the symmetry permutation subgroup in Pyraminx. First, it is proved that movements in Pyraminx form group using 2 methods, namely direct proof in Pyraminx (Pyaminx movement group) and performing permutations in set containing numeric labels in the form of numbers 1 to 36 on Pyraminx facets by following the movements of Pyraminx ( symmetry permutation subgroup). Furthermore, it is proved that there is a group isomorphism from the Pyraminx movement group to the symmetry permutation subgroup in Pyraminx.

Keywords

Collaboration network of the authors

26 authors · 43 co-authorship links · 1 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Telkom University
  • Universitas Halu Oleo
  • Hasanuddin University
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Nur ErawatiAffiliation unknown2
Nurdin HindingAffiliation unknown2
Hasmawati HasmawatiTelkom University2
Jeriko GormantaraAffiliation unknown1
Hanni GarminiaAffiliation unknown1
Evan RamdanAffiliation unknown1
Afriani AfrianiAffiliation unknown1
Qharnida KharianiAffiliation unknown1
Hasmawati BasirAffiliation unknown1
winda aritonangAffiliation unknown1
Armin LawiHasanuddin University1
Nurhidayah NurhidayahUniversitas Halu Oleo1
Mawardi BahriAffiliation unknown1
Yudhiyanto SupriadiAffiliation unknown1
Budi NurwahyuAffiliation unknown1
Ahmad Syukur DamingAffiliation unknown1
St. Munieroh FachrunnisaAffiliation unknown1
Aidah Nabilah AnwarAffiliation unknown1
Andi Muhammad AnwarAffiliation unknown1
Jeki SaputraAffiliation unknown1
I Made SudanaAffiliation unknown1
Cahyo Budi UtomoAffiliation unknown1
Wilma Rahmah HidayatiAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Group and Group Isomorphism in Pyraminx</dc:title>
	<dc:title xml:lang="id">Grup dan Isomorfisma Grup pada Pyraminx</dc:title>
	<dc:creator xml:lang="en">Nurhafizah, Nurhafizah</dc:creator>
	<dc:creator xml:lang="en">Erawaty, Nur </dc:creator>
	<dc:creator xml:lang="en">Amir, Amir Kamal </dc:creator>
	<dc:subject xml:lang="en">Group</dc:subject>
	<dc:subject xml:lang="en">S36 symmetry permutation group</dc:subject>
	<dc:subject xml:lang="en">subgroup</dc:subject>
	<dc:subject xml:lang="en">isomorphism</dc:subject>
	<dc:subject xml:lang="en">Pyraminx</dc:subject>
	<dc:description xml:lang="en">Pyraminx is a twisty puzzle in the shape of a tetrahedron with 4 sides. Pyraminx is played with the bottom completely flat and the front side facing the person holding the Pyraminx. The goal of the Pyraminx game is to randomize the colors, then return the scrambled colors to their original color positions by rotating the sides. This research does not discuss the most effective way of solving Pyraminx but focuses more on proving that movements in Pyraminx form group and that there is a group isomorphism from the group of Pyraminx movements to the  symmetry permutation subgroup in Pyraminx. First, it is proved that movements in Pyraminx form group using 2 methods, namely direct proof in Pyraminx (Pyaminx movement group) and performing permutations in set   containing numeric labels in the form of numbers 1 to 36 on Pyraminx facets by following the movements of Pyraminx ( symmetry permutation subgroup). Furthermore, it is proved that there is a group isomorphism from the Pyraminx movement group to the   symmetry permutation subgroup in Pyraminx.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2023-12-24</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/30320</dc:identifier>
	<dc:identifier>10.20956/j.v20i2.30320</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 20 No. 2 (2024): JANUARY 2024; 455-466</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/30320/10964</dc:relation>
	<dc:relation>10.20956/j.v20i2.30320.g10964</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>