What question did this study set out to answer?

To introduce and define the term 'quadroject' for the process of extending 3D objects into the fourth dimension.

May 26, 20260 citationsOpen Access

Quadroject: A formal resolution framework for self-contradictory systems

Key Points

To introduce and define the term 'quadroject' for the process of extending 3D objects into the fourth dimension.
Provided definitions for verb and noun forms of 'quadroject'.
Illustrated the concept with examples including a tesseract and a glome.
Discussed the term's application in math education and speculative physics.
'Quadroject' clearly differentiates general 4D extrusion from specific cases like 'tesseract'.
The term serves as a useful addition in science communication.
Coined in 2026 to fill a lexical gap in discussing four-dimensional objects.

Abstract

AbstractEnglish lacks a concise term for the general operation of extending an arbitrary three-dimensional object into the fourth spatial dimension. I propose the neologism “quadroject” to fill this lexical gap and provide definitions for both verb and noun forms. 1. DefinitionVerb: To quadroject is to extrude or extend a three-dimensional object into the fourth spatial dimension.Example: To quadroject a cube yields a tesseract. Noun: A quadroject is the four-dimensional object resulting from the extrusion of a three-dimensional object into 4D.Example: The quadroject of a sphere is a glome, also known as a 3-sphere. 2. EtymologyFrom Latin quadro- (“four”) + English project (“to throw forward”). Coined in 2026 by Nicolas David Malone.3. Usage and DistinctionThe term distinguishes the general 4D extrusion operation from the specific case “tesseract,” which refers only to the 4D hypercube. This parallels how “polygon” is general while “square” is specific. The term is intended for use in mathematics education, science communication, and speculative physics. 4. Date of Coinage24 May 2026 License: Creative Commons Attribution International

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