Daftar bentuk matematika

Dimensi	Cembung	Takcembung	Teselasi cembung Euklides	Teselasi cembung hiperbolik	Teselasi takcembung hiperbolik	Teselasi Hiperbolik dengan sel takhingga dan/atau gambar verteks	Politop abstrak
1	1 ruas garis	0	1	0	0	0	1
2	∞ polygons	∞ star polygons	1	1	0	0	∞
3	5 Platonic solids	4 Kepler–Poinsot solids	3 tilings	∞	∞	∞	∞
4	6 convex polychora	10 Schläfli–Hess polychora	1 honeycomb	4	0	11	∞
5	3 convex 5-polytopes	0	3 tetracombs	5	4	2	∞
6	3 convex 6-polytopes	0	1 pentacombs	0	0	5	∞
7+	3	0	1	0	0	0	∞

There are no nonconvex Euclidean regular tessellations in any number of dimensions.

Polytope elements[sunting | sunting sumber]

The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.

Puncak, sebuah elemen dimensi 0
Sisi, sebuah elemen dimensi 1
Wajah, sebuah elemen dimensi 2
Sel, sebuah elemen dimensi 3
Hipersel, sebuah elemen dimensi 4
Facet, sebuah (n-1)
Ridge, sebuah elemen dimensi (n-2)
Peak, sebuah elemen dimensi (n-3)

For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak.

Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.

Teselasi[sunting | sunting sumber]

The classical convex polytopes may be considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.

Dimensi nol[sunting | sunting sumber]

Titik (geometri)

Politop regular satu dimensi[sunting | sunting sumber]

Terdapat hanya satu politop dalam 1 dimensi, yang batasnya terdapat dua titik akhir ruas garis, diwakili oleh simbol Schläfli kosong {}.

Politop regular dua dimensi[sunting | sunting sumber]

Cembung[sunting | sunting sumber]

Merosot (bola)[sunting | sunting sumber]

Takcembung[sunting | sunting sumber]

Degenerate (spherical)[sunting | sunting sumber]

Takcembung[sunting | sunting sumber]

Kepler–Poinsot polyhedra

Tessellations[sunting | sunting sumber]

Euclidean tilings[sunting | sunting sumber]

Hyperbolic tilings[sunting | sunting sumber]

Hyperbolic star-tilings[sunting | sunting sumber]

Four-dimensional regular polytopes[sunting | sunting sumber]

convex regular 4-polytope
- 5-cell, the 4-space Simplex
- 8-cell, the 4-space Hypercube
- 16-cell, the 4-space Cross-polytope
- 24-cell
- 120-cell
- 600-cell

Degenerate (spherical)[sunting | sunting sumber]

Non-convex[sunting | sunting sumber]

Star or (Schläfli–Hess) regular 4-polytope

Tessellations of Euclidean 3-space[sunting | sunting sumber]

Degenerate tessellations of Euclidean 3-space[sunting | sunting sumber]

Tessellations of hyperbolic 3-space[sunting | sunting sumber]

Five-dimensional regular polytopes and higher[sunting | sunting sumber]

Simplex	Hypercube	Cross-polytope
5-simplex	5-cube	5-orthoplex
6-simplex	6-cube	6-orthoplex
7-simplex	7-cube	7-orthoplex
8-simplex	8-cube	8-orthoplex
9-simplex	9-cube	9-orthoplex
10-simplex	10-cube	10-orthoplex
11-simplex	11-cube	11-orthoplex