Jump to content

User:Tomruen/mixed polytopes

From Wikipedia, the free encyclopedia
Polygons
Family Form Example Family Form Example
rectangle
2-orthotope
{ }×{ }

[2]
2-cube
t{2}
rhombus
2-fusil
{ }+{ }

[2]
2-orthoplex
Polyhedra Polychora
Family Form Example Family Form Family Form Example Family Form Example
pyramid {n}∨()
[n,1]
triangular pyramid
{3}∨() as tetrahedron
digonal
disphenoid
{ }∨{ }
[2]
pyramid {p,q}∨()
[p,q,1]
tetrahedral pyramid
{3,3}∨() as 5-cell
{p}∨{ }
[p,2,1]
tetrahedral pyramid
{3}∨{ } as 5-cell
Polyhedra Polychora
Family Form Example Family Form Example Family Form Example
prism { }×{n}
=t{2,n}

[2,n]
square prism
{ }×{4} as cube
= t{2,4}
prism { }×{p,q}
=t{2,p,q}

[2,p,q]
cubic prism
{ }×{4,3} as tesseract
= t{2,4,3}
duoprism {p}×{q}
=rr{p,2,q}

[p,2,q]
4-4 duoprism
{4}×{4} as tesseract
= rr{4,2,4}
bipyramid
(fusil)
{ }+{n}

[2,n]
square fusil
{ }+{4} as octahedron
bipyramid
(fusil)
{ }+{p,q}

[2,p,q]
octahedral fusil
{ }+{3,4} as 16-cell
duopyramid
(duofusil)
{p}+{q}

[p,2,q]
4-4 duofusil
{4}+{4} as 16-cell
antiprism { }⨂{n}
=h{2}s{n}
=s{2,2n}

[2,n]+

[2+,2n]
triangular antiprism
{ }⨂{3} as octahedron
= h{2}s{3}
= s{2,6}
antiprism { }⨂{p,2q}
=h{2}s{p,2q}

[(2,p)+,2q]
snub octahedral antiprism
{ }⨂{3,4}
= h{2}s{3,4}
duoantiprism {p}⨂{q}
=s{p}s{q}
=2s{2p,2,2q}

[p,2,q]+

[2p,2+,2q]
2-2 duoantiprism
{2}⨂{2} as 16-cell
= s{2}s{2}
= 2s{4,2,4}
trapezohedron
(antifusil)
{ }⨁{n}

[2,n]+

[2+,2n]
triangular antifusil
{ }⨁{3} as cube

antifusil { }⨁{p,2q}

[(2,p)+,q]
snub octahedral antifusil
{ }⨁{3,4} as icosahedral antifusil
duoantifusil {p}⨁{q}

[p,2,q]+

[2p,2+,2q]
2-2 duoantifusil
{2}⨁{2} as tesseract


Polyhedra Polychora
Family Example Image Family Example
Prism
{ }×{n}
[2,n], order 4n
Square prism
{ }×{4} as cube
[2,4], order 16
Duoprism
{p}×{q}
[p,2,q], order 4pq
[[p,2,p]], order 8p2
4-4 duoprism
{4}×{4} as tesseract
[4,2,4], order 64
[[4,2,4]], order 128
Fusil
{ }+{n}
[2,n], order 4n
Square fusil
{ }+{4} as octahedron
[2,4], order 16
Duofusil
{p}+{q}
[p,2,q], order 4pq
[[p,2,p]], order 8p2
4-4 duofusil
{4}+{4} as 16-cell
[4,2,4], order 64
[[4,2,4]], order 128
Antiprism
{ }⨂{n}
[2,n]+, order 2n
[2+,2n], order 4n
Triangular antiprism
{ }⨂{3} as octahedron
[2,3]+, order 6
[2+,6], order 12
Duoantiprism
{p}⨂{q}
[p,2,q]+, order 2pq
[2p,2+,2q], order 8pq
[[2p,2+,2p]], order 16p2
2-2 duoantiprism
{2}⨂{2} as 16-cell
[2,2,2]+, order 8
[4,2+,4], order 32
[[4,2+,4]], order 64
Antifusil
{ }⨁{n}
[2,n]+, order 2n
[2+,2n], order 4n
Triangular antifusil
{ }⨁{3} as cube
[2,3]+, order 6
[2+,6], order 12
Duoantifusil
{p}⨁{q}
[p,2,q]+, order 2pq
[2p,2+,2q], order 8pq
[[2p,2+,2p]], order 16p2
2-2 duoantifusil
{2}⨁{2} as tesseract
[2,2,2]+, order 8
[4,2+,4], order 32
[[4,2+,4]], order 64

Pyramid, fusil, prism

[edit]
Pyramid Fusil Prism Type
Operator Join Rhombic sum Rectangular product
Symbol P ∨ Q P + Q P × Q
Dimension a+b+1 a+b
1D ( ) ∨ ( ) = 2.( )
Ditel
[ ]
{ }
Ditel
[ ]
2D ( ) ∨ { }
Isosceles triangle
[1]
{ } + { } = 2{ }
Rhombus
[2]
{ } × { } = { }2
Rectangle
[2]
3D { } ∨ { } = 2.{ }
Digonal disphenoid
[1,2]
{ } + {p}
p-gonal fusil
(p bipyramid)
[2,p]
{ } × {p}
p-gonal prism
(p prism)
[2,p]
4D { } ∨ {p}
p-gonal pyramid
(p pyramid)
[1,2,p]
{p} + {q}
p-gonal q-gonal fusil
(p-q duofusil)
[p,2,q]
{p} × {q}
p-gonal q-gonal prism
(p-q duoprism)
[p,2,q]
2{p}
p-gonal double fusil
(p-p duofusil)
[[p,2,q]]
{p}2
p-gonal double prism
(p-p duoprism)
[[p,2,q]]
5D {p} ∨ {q}
p-gonal q-gonal pyramid
(p-q duopyramid)
[1,p,2,q]
2.{p}
p-gonal double pyramid
(p-p duopyramid)
[1,[p,2,p]]