EulerCharacteristic
P39244
predicate
Indicates the topological invariant of a space that equals, in a suitable decomposition, the alternating sum of the counts of its cells (e.g., vertices − edges + faces).
All labels observed (3)
| Label | Occurrences |
|---|---|
| hasEulerCharacteristic | 6 |
| EulerCharacteristic canonical | 4 |
| haveEulerCharacteristic | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: EulerCharacteristic
Generated description
Indicates the topological invariant of a space that equals, in a suitable decomposition, the alternating sum of the counts of its cells (e.g., vertices − edges + faces).
Sample triples (11)
| Subject | Object |
|---|---|
| Klein quartic | -4 ⓘ |
| Euler’s polyhedron formula | 2 via predicate surface "hasEulerCharacteristic" ⓘ |
| Kepler–Poinsot polyhedra | non-standard when faces and vertices are counted naively via predicate surface "haveEulerCharacteristic" ⓘ |
| Riemann sphere | 2 ⓘ |
|
Clebsch diagonal surfaces
surface form:
Clebsch diagonal surface
|
3 via predicate surface "hasEulerCharacteristic" ⓘ |
|
Kummer surfaces
surface form:
Kummer surface
|
24 ⓘ |
| Fermat surface | topological Euler characteristic depending polynomially on n via predicate surface "hasEulerCharacteristic" ⓘ |
| rhombicuboctahedron | 2 via predicate surface "hasEulerCharacteristic" ⓘ |
| rhombicosidodecahedron | 2 via predicate surface "hasEulerCharacteristic" ⓘ |
|
Hurwitz surfaces
surface form:
Hurwitz surface
|
2−2g via predicate surface "hasEulerCharacteristic" ⓘ |
| 4-sphere S^4 | 2 ⓘ |