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Roman surface

In mathematics, the Roman surface or Steiner surface is a self-intersecting mapping of the real projective plane into three-dimensional space, with an unusually high degree of symmetry. This mapping is not an immersion of the projective plane; however, the figure resulting from removing six singular points is one. Its name arises because it was…

Overview, Structure of the Roman surface & One-sidedness

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Overview

MathematicsMappingReal projective planeThree-dimensional spaceSymmetry
18 related topics

Structure of the Roman surface

Hyperbolic paraboloidsOriginOrchidsBulbous
4 related topics

One-sidedness

OrientableAntHyperbolic paraboloidKlein bottle
4 related topics

Derivation of implicit formula

Without loss of generalityAbsolute value
2 related topics

Topics to explore

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Overview

Derivation of implicit formula

Relation to the real projective plane

Structure of the Roman surface

One-sidedness

Double, triple, and pinching points

General references

Advanced semantic analysis

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Map overview Semantic statistics

Roman surface

Nodes41
Edges40
Triples39
Avg. degree1.95
Density0.04878
Components1

How this topic connects Entity context

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Roman surface

Top relations

related to One-sidedness · 13
Roman surface → As, Figure, Imagine, It, Let, North, Roman, So, The, The Roman, These, This, To
related to External links · 11
Roman surface → Ashay Dharwadker, California State University, Coffman, Electronic Geometry Models, Eric, Heptahedron, MathWorld, National Curve Bank, Roman Surfaces, Steiner Surfaces, Weisstein
related to Double, triple, and pinching points · 9
Roman surface → Between, But, If, One, Roman, The, The Roman, These, Whitney
see also · 3
Roman surface → Boy's, Roman, Tetrahemihexahedron
related to Structure of the Roman surface · 2
Roman surface → Roman, The Roman
is a · 1
Roman surface → continuous image of a

Important terminology Word statistics

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Important terminology

surface points roman figure ant lobes double three displaystyle one xy point plane sphere paraboloids yz origin lobe axis triple

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Roman surfaceis acontinuous image of a0.90text
Roman surfacerelated to Double, triple, and pinching pointsThe Roman0.60section
Roman surfacerelated to Double, triple, and pinching pointsThe0.60section
Roman surfacerelated to Double, triple, and pinching pointsBetween0.60section
Roman surfacerelated to Double, triple, and pinching pointsOne0.60section
Roman surfacerelated to Double, triple, and pinching pointsBut0.60section
Roman surfacerelated to Double, triple, and pinching pointsIf0.60section
Roman surfacerelated to Double, triple, and pinching pointsRoman0.60section
Roman surfacerelated to Double, triple, and pinching pointsWhitney0.60section
Roman surfacerelated to Double, triple, and pinching pointsThese0.60section
Roman surfacerelated to External linksCoffman0.60section
Roman surfacerelated to External linksSteiner Surfaces0.60section

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    Min side: 3
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