A tesseract or octachoron is a fourth-dimensional hypercube. Since the number of dimensions is a square number, the diagonal length of a tesseract is an integer - in this case, 2. Its Bowers acronym is "tes ". It is one of the three regular polychora that can tile 4-dimensional space, forming the tesseractic tetracomb . Under the elemental naming scheme it is called a geochoron .
Tesseract Rubik's cubes can found online , but cannot be built in the 3D world.
Hypercube Products [ ] The tesseract can be expressed as a hypercube product, potentially with less symmetry than the uniform and regular ideal tesseract, in five different ways:
{
4
,
3
,
3
}
{\displaystyle \{4, 3, 3\}}
[ ] As a tesseract, the hypervolumes can be expressed in terms of a single variable, the edge length l. This is the most symmetrical variant of the tesseract.
{
4
,
3
}
×
{
}
{\displaystyle \{4,3\} \times \{\}}
[ ] As a cube prism, the hypervolumes require two lengths to express: the edge length a of the cube, and the height b of the prism.
edge length =
8
(
3
a
+
b
)
{\displaystyle 8\left(3a + b\right)}
surface area =
12
a
(
a
+
b
)
{\displaystyle 12a \left( a + b \right)}
surcell volume =
2
a
2
(
a
+
3
b
)
{\displaystyle 2a^2 \left( a + 3b \right)}
surteron bulk =
a
3
b
{\displaystyle a^3 b}
When a=b, this becomes the symmetrical tesseract.
{
4
}
×
{
}
2
{\displaystyle \{4\} \times \{\}^2}
[ ] As a square prism prism, the hypervolumes require three lengths to express: the edge length a of the square, and the seperate heights b and c of the two prisms.
edge length =
8
(
2
a
+
b
+
c
)
{\displaystyle 8 \left( 2a + b + c \right)}
surface area =
4
(
a
2
+
2
a
b
+
2
a
c
+
b
c
)
{\displaystyle 4 \left( a^2 + 2 ab + 2 ac + bc \right)}
surcell volume =
2
a
(
a
b
+
a
c
+
2
b
c
)
{\displaystyle 2a \left( ab + ac + 2bc \right)}
surteron bulk =
a
2
b
c
{\displaystyle a^2 b c}
When a=b xor a=c, this becomes the cubic prism. When b=c, this becomes the square duoprism. When a=b=c, this becomes the symmetrical tesseract.
{
}
4
{\displaystyle \{\}^4}
[ ] As a line prism prism prism, the hypervolumes require four lengths to express. This is the least symmetrical variant of the tesseract.
edge length =
8
(
a
+
b
+
c
+
d
)
{\displaystyle 8\left( a + b + c + d \right)}
surface area =
4
(
a
b
+
a
c
+
a
d
+
b
c
+
b
d
+
c
d
)
{\displaystyle 4 \left( ab + ac + ad + bc + bd + cd \right) }
surcell volume =
2
(
a
b
c
+
a
b
d
+
a
c
d
+
b
c
d
)
{\displaystyle 2 \left( abc + abd + acd + bcd \right)}
surteron bulk =
a
b
c
d
{\displaystyle abcd}
When a=b and c=d, a=c and b=d, xor a=d and b=c, this becomes the square duoprism. When a=b=c, b=c=d, a=c=d xor a=b=d, this becomes the cubic prism. When a=b, a=c, a=d, b=c, b=d xor c=d, this becomes the square prism prism. When a=b=c=d, this becomes the symmetrical tesseract.
{
4
}
2
{\displaystyle \{4\}^2}
[ ] As a square duoprism, the hypervolumes require two lengths to express: the seperate edge lengths a and b of the two squares.
edge length =
16
(
a
+
b
)
{\displaystyle 16 \left( a + b \right)}
surface area =
4
(
a
2
+
4
a
b
+
b
2
)
{\displaystyle 4 \left( a^2 + 4 ab + b^2 \right)}
surcell volume =
4
a
b
(
a
+
b
)
{\displaystyle 4ab \left( a + b \right)}
surteron bulk =
a
2
b
2
{\displaystyle a^2 b^2}
When a=b, this becomes the symmetrical tesseract.
Properties [ ] The tesseract can be exactly decomposed into eight cubic pyramids with unit side length. This is because the distance between a vertex and the center is the same as the edge length. If these pyramids are joined to the cubes of the tesseract the result is the icositetrachoron - the square pyramidal cells merge into octahedra.
Symbols [ ] Dynkin symbols of the tesseract include:
x4o3o3o (regular)
x x4o3o (cubic prism)
x4o x4o (square duoprism)
x x x4o (square diprism)
x x x x (tesseractic block)
xx4oo3oo&#xt, xx xx4oo&#xt, xx xx xx&#xt (as cube atop cube)
oqooo3ooqoo3oooqo&#xt (vertex first)
xxx4ooo oqo&#xt, xxx xxx oqo&#xt (square first)
xxxx oqoo3ooqo&#xt (edge first)
qo3oo3oq *b3oo&#zx (sum of two demitesseracts)
xx xx qo oq&#zx (rhombic diprism)
xx qo3oo3oq&#zx *prism of sum of two tetrahedra) Structure and Sections [ ] Structure [ ] The tesseract is composed of 8 cubic cells. Two of these cubes line in parallel 3-D spaces, while the remaining six connect the faces of the cubes. Four cubes meet at each vertex.
In cube-first position, it is a sequence of identical cubes. In square-centered orientation, it is a square which expands to a square prism and back. When seen line-first it is a line that expands to a triangular prism , then turns to a hexagonal prism , and then back. Finally in corner first orientation, it goes through the entire tetrahedral truncation series, from point to tetrahedron to octahedron in the middle and then back.
Hypervolumes [ ] Subfacets [ ] Radii [ ] Vertex radius:
l
{\displaystyle l}
Edge radius:
3
2
l
{\displaystyle \frac{\sqrt{3}}{2}l}
Face radius:
2
2
l
{\displaystyle \frac{\sqrt{2}}{2}l}
Cell radius:
1
/
2
l
{\displaystyle 1/2l}
Angles [ ] Vertex coordinates [ ] The vertices of a tesseract with side 2 can be denoted on a 4D Cartesian plane by (±1,±1,±1,±1).
Equations [ ] The surface of a tesseract can be graphed by the equation
m
a
x
(
x
2
,
y
2
,
z
2
,
w
2
)
=
1
{\displaystyle max(x^2,y^2,z^2,w^2) = 1}
Notations [ ] Toratopic notation:
|
|
|
|
{\displaystyle ||||}
Tapertopic notation:
1111
{\displaystyle 1111}
Related shapes [ ] See Also [ ]
Dimensionality
Negative One
Zero
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Eleven
Twelve
Thirteen
Fourteen
Fifteen
Sixteen
Seventeen
...
Aleph null
Simplex
{
3
n
−
1
}
{\displaystyle \{3^{n-1}\}}
Null polytope
)
(
{\displaystyle )(}
∅
{\displaystyle \emptyset}
Point
(
)
{\displaystyle ()}
B
0
{\displaystyle \mathbb{B}^0}
Line segment
{
}
{\displaystyle \{\}}
B
1
{\displaystyle \mathbb{B}^1}
Triangle
{
3
}
{\displaystyle \{3\}}
Tetrahedron
{
3
2
}
{\displaystyle \{3^2\}}
Pentachoron
{
3
3
}
{\displaystyle \{3^3\}}
Hexateron
{
3
4
}
{\displaystyle \{3^4\}}
Heptapeton
{
3
5
}
{\displaystyle \{3^5\}}
Octaexon
{
3
6
}
{\displaystyle \{3^6\}}
Enneazetton
{
3
7
}
{\displaystyle \{3^7\}}
Decayotton
{
3
8
}
{\displaystyle \{3^8\}}
Hendecaxennon
{
3
9
}
{\displaystyle \{3^9\}}
Dodecadakon
{
3
10
}
{\displaystyle \{3^{10}\}}
Tridecahendon
{
3
11
}
{\displaystyle \{3^{11}\}}
Tetradecadokon
{
3
12
}
{\displaystyle \{3^{12}\}}
Pentadecatradakon
{
3
13
}
{\displaystyle \{3^{13}\}}
Hexadecatedakon
{
3
14
}
{\displaystyle \{3^{14}\}}
Heptadecapedakon
{
3
15
}
{\displaystyle \{3^{15}\}}
Octadecapedakon
{
3
16
}
{\displaystyle \{3^{16}\}}
...
Omegasimplex
Cross
{
3
n
−
2
,
4
}
{\displaystyle \{3^{n-2},4\}}
Square
{
4
}
{\displaystyle \{4\}}
Octahedron
{
3
,
4
}
{\displaystyle \{3, 4\}}
Hexadecachoron
{
3
2
,
4
}
{\displaystyle \{3^2, 4\}}
Pentacross
{
3
3
,
4
}
{\displaystyle \{3^3, 4\}}
Hexacross
{
3
4
,
4
}
{\displaystyle \{3^4, 4\}}
Heptacross
{
3
5
,
4
}
{\displaystyle \{3^5, 4\}}
Octacross
{
3
6
,
4
}
{\displaystyle \{3^6, 4\}}
Enneacross
{
3
7
,
4
}
{\displaystyle \{3^7, 4\}}
Dekacross
{
3
8
,
4
}
{\displaystyle \{3^8, 4\}}
Hendekacross
{
3
9
,
4
}
{\displaystyle \{3^9, 4\}}
Dodekacross
{
3
10
,
4
}
{\displaystyle \{3^{10}, 4\}}
Tridekacross
{
3
11
,
4
}
{\displaystyle \{3^{11}, 4\}}
Tetradekacross
{
3
12
,
4
}
{\displaystyle \{3^{12}, 4\}}
Pentadekacross
{
3
13
,
4
}
{\displaystyle \{3^{13}, 4\}}
Hexadekacross
{
3
14
,
4
}
{\displaystyle \{3^{14}, 4\}}
Heptadekacross
{
3
15
,
4
}
{\displaystyle \{3^{15},4\}}
...
Omegacross
Hydrotopes
{
3
n
−
2
,
5
}
{\displaystyle \{3^{n-2}, 5\}}
Pentagon
{
5
}
{\displaystyle \{5\}}
Icosahedron
{
3
,
5
}
{\displaystyle \{3, 5\}}
Hexacosichoron
{
3
2
,
5
}
{\displaystyle \{3^2, 5\}}
Order-5 pentachoric tetracomb
{
3
3
,
5
}
{\displaystyle \{3^3, 5\}}
Order-5 hexateric pentacomb
{
3
4
,
5
}
{\displaystyle \{3^4, 5\}}
...
Hypercube
{
4
,
3
n
−
2
}
{\displaystyle \{4, 3^{n-2}\}}
Square
{
4
}
{\displaystyle \{4\}}
Cube
{
4
,
3
}
{\displaystyle \{4,3\}}
Tesseract
{
4
,
3
2
}
{\displaystyle \{4, 3^2\}}
Penteract
{
4
,
3
3
}
{\displaystyle \{4, 3^3\}}
Hexeract
{
4
,
3
4
}
{\displaystyle \{4, 3^4\}}
Hepteract
{
4
,
3
5
}
{\displaystyle \{4, 3^5\}}
Octeract
{
4
,
3
6
}
{\displaystyle \{4, 3^6\}}
Enneract
{
4
,
3
7
}
{\displaystyle \{4, 3^7\}}
Dekeract
{
4
,
3
8
}
{\displaystyle \{4, 3^8\}}
Hendekeract
{
4
,
3
9
}
{\displaystyle \{4, 3^9\}}
Dodekeract
{
4
,
3
10
}
{\displaystyle \{4, 3^{10}\}}
Tridekeract
{
4
,
3
11
}
{\displaystyle \{4, 3^{11}\}}
Tetradekeract
{
4
,
3
12
}
{\displaystyle \{4, 3^{12}\}}
Pentadekeract
{
4
,
3
13
}
{\displaystyle \{4, 3^{13}\}}
Hexadekeract
{
4
,
3
14
}
{\displaystyle \{4, 3^{14}\}}
Heptadekeract
{
4
,
3
15
}
{\displaystyle \{4,3^{15}\}}
...
Omegeract
Cosmotopes
{
5
,
3
n
−
2
}
{\displaystyle \{5, 3^{n-2}\}}
Pentagon
{
5
}
{\displaystyle \{5\}}
Dodecahedron
{
5
,
3
}
{\displaystyle \{5, 3\}}
Hecatonicosachoron
{
5
,
3
2
}
{\displaystyle \{5, 3^2\}}
Order-3 hecatonicosachoric tetracomb
{
5
,
3
3
}
{\displaystyle \{5, 3^3\}}
Order-3-3 hecatonicosachoric pentacomb
{
5
,
3
4
}
{\displaystyle \{5, 3^4\}}
...
Hyperball
B
n
{\displaystyle \mathbb B^n}
Disk
B
2
{\displaystyle \mathbb B^2}
Ball
B
3
{\displaystyle \mathbb B^3}
Gongol
B
4
{\displaystyle \mathbb B^4}
Pentorb
B
5
{\displaystyle \mathbb B^5}
Hexorb
B
6
{\displaystyle \mathbb B^6}
Heptorb
B
7
{\displaystyle \mathbb B^7}
Octorb
B
8
{\displaystyle \mathbb B^8}
Enneorb
B
9
{\displaystyle \mathbb B^9}
Dekorb
B
10
{\displaystyle \mathbb B^{10}}
Hendekorb
B
11
{\displaystyle \mathbb B^{11}}
Dodekorb
B
12
{\displaystyle \mathbb B^{12}}
Tridekorb
B
13
{\displaystyle \mathbb B^{13}}
Tetradekorb
B
14
{\displaystyle \mathbb B^{14}}
Pentadekorb
B
15
{\displaystyle \mathbb B^{15}}
Hexadekorb
B
16
{\displaystyle \mathbb B^{16}}
Heptadekorb
B
17
{\displaystyle \mathbb {B} ^{17}}
...
Omegaball
B
ℵ
0
{\displaystyle \mathbb B^{\aleph_0}}
{
2
,
3
,
3
}
{\displaystyle \{2,3,3\}}
{
3
,
3
,
3
}
{\displaystyle \{3,3,3\}}
{
4
,
3
,
3
}
{\displaystyle \{4, 3, 3\}}
{
5
,
3
,
3
}
{\displaystyle \{5,3,3\}}
{
6
,
3
,
3
}
{\displaystyle \{6,3,3\}}
Tetrahedral hosochoron
Pentachoron
Tesseract
Hecatonicosachoron
Order-3 hexagonal tiling honeycomb
{
4
,
3
,
2
}
{\displaystyle \{4,3,2\}}
{
4
,
3
,
3
}
{\displaystyle \{4, 3, 3\}}
{
4
,
3
,
4
}
{\displaystyle \{4,3,4\}}
{
4
,
3
,
5
}
{\displaystyle \{4,3,5\}}
{
4
,
3
,
6
}
{\displaystyle \{4,3,6\}}
Cubic dichoron
Tesseract
Cubic honeycomb
Order-5 cubic honeycomb
Order-6 cubic honeycomb
Regular
t
0
{
4
,
3
,
3
}
{\displaystyle t_0 \{4,3,3\}}
Rectified
t
1
{
4
,
3
,
3
}
{\displaystyle t_1 \{4,3,3\}}
Birectified
t
2
{
4
,
3
,
3
}
{\displaystyle t_2 \{4,3,3\}}
Trirectified
t
3
{
4
,
3
,
3
}
{\displaystyle t_3 \{4,3,3\}}
Truncated
t
0
,
1
{
4
,
3
,
3
}
{\displaystyle t_{0,1} \{4,3,3\}}
Bitruncated
t
1
,
2
{
4
,
3
,
3
}
{\displaystyle t_{1,2} \{4,3,3\}}
Tritruncated
t
2
,
3
{
4
,
3
,
3
}
{\displaystyle t_{2,3} \{4,3,3\}}
Tesseract
Rectified tesseract
Icositetrachoron
Hexadecachoron
Truncated tesseract
Bitruncated tesseract
Truncated hexadecachoron
Cantellated
t
0
,
2
{
4
,
3
,
3
}
{\displaystyle t_{0,2} \{4,3,3\}}
Bicantellated
t
1
,
3
{
4
,
3
,
3
}
{\displaystyle t_{1,3} \{4,3,3\}}
Cantitruncated
t
0
,
1
,
2
{
4
,
3
,
3
}
{\displaystyle t_{0,1,2} \{4,3,3\}}
Bicantitruncated
t
1
,
2
,
3
{
4
,
3
,
3
}
{\displaystyle t_{1,2,3} \{4,3,3\}}
Runcinated
t
0
,
3
{
4
,
3
,
3
}
{\displaystyle t_{0,3} \{4,3,3\}}
Runcicantellated
t
0
,
2
,
3
{
4
,
3
,
3
}
{\displaystyle t_{0,2,3} \{4,3,3\}}
Runcitruncated
t
0
,
1
,
3
{
4
,
3
,
3
}
{\displaystyle t_{0,1,3} \{4,3,3\}}
Runcicantitruncated
t
0
,
1
,
2
,
3
{
4
,
3
,
3
}
{\displaystyle t_{0,1,2,3} \{4,3,3\}}
Cantellated tesseract
Rectified icositetrachoron
Cantitruncated tesseract
Truncated icositetrachoron
Runcinated tesseract
Runcitruncated hexadecachoron
Runcitruncated tesseract
Omnitruncated tesseract
Regular
t
0
{
4
,
3
,
2
}
{\displaystyle t_0 \{4,3,2\}}
Rectified
t
1
{
4
,
3
,
2
}
{\displaystyle t_1 \{4,3,2\}}
Birectified
t
2
{
4
,
3
,
2
}
{\displaystyle t_2 \{4,3,2\}}
Trirectified
t
3
{
4
,
3
,
2
}
{\displaystyle t_3 \{4,3,2\}}
Truncated
t
0
,
1
{
4
,
3
,
2
}
{\displaystyle t_{0,1} \{4,3,2\}}
Bitruncated
t
1
,
2
{
4
,
3
,
2
}
{\displaystyle t_{1,2} \{4,3,2\}}
Tritruncated
t
2
,
3
{
4
,
3
,
2
}
{\displaystyle t_{2,3} \{4,3,2\}}
Cubic dichoron
Rectified cubic dichoron
Rectified octahedral hosochoron
Octahedral hosochoron
Truncated cubic dichoron
Bitruncated cubic dichoron
Octahedral prism
Cantellated
t
0
,
2
{
4
,
3
,
2
}
{\displaystyle t_{0,2} \{4,3,2\}}
Bicantellated
t
1
,
3
{
4
,
3
,
2
}
{\displaystyle t_{1,3} \{4,3,2\}}
Cantitruncated
t
0
,
1
,
2
{
4
,
3
,
2
}
{\displaystyle t_{0,1,2} \{4,3,2\}}
Bicantitruncated
t
1
,
2
,
3
{
4
,
3
,
2
}
{\displaystyle t_{1,2,3} \{4,3,2\}}
Runcinated
t
0
,
3
{
4
,
3
,
2
}
{\displaystyle t_{0,3} \{4,3,2\}}
Runcicantellated
t
0
,
2
,
3
{
4
,
3
,
2
}
{\displaystyle t_{0,2,3} \{4,3,2\}}
Runcitruncated
t
0
,
1
,
3
{
4
,
3
,
2
}
{\displaystyle t_{0,1,3} \{4,3,2\}}
Runcicantitruncated
t
0
,
1
,
2
,
3
{
4
,
3
,
2
}
{\displaystyle t_{0,1,2,3} \{4,3,2\}}
Cantellated cubic dichoron
Cuboctahedral prism
Cantitruncated cubic dichoron
Truncated octahedral prism
Tesseract
Rhombicuboctahedral prism
Truncated cubic prism
Great rhombicuboctahedral prism
Regular
t
0
{
4
,
2
,
4
}
{\displaystyle t_0 \{4,2,4\}}
Rectified
t
1
{
4
,
2
,
4
}
{\displaystyle t_1 \{4,2,4\}}
Birectified
t
2
{
4
,
2
,
4
}
{\displaystyle t_2 \{4,2,4\}}
Trirectified
t
3
{
4
,
2
,
4
}
{\displaystyle t_3 \{4,2,4\}}
Truncated
t
0
,
1
{
4
,
2
,
4
}
{\displaystyle t_{0,1} \{4,2,4\}}
Bitruncated
t
1
,
2
{
4
,
2
,
4
}
{\displaystyle t_{1,2} \{4,2,4\}}
Tritruncated
t
2
,
3
{
4
,
2
,
4
}
{\displaystyle t_{2,3} \{4,2,4\}}
Square tetrachoron
Rectified square tetrachoron
Rectified square tetrachoron
Square tetrachoron
Truncated square tetrachoron
Tesseract
Truncated square tetrachoron
Cantellated
t
0
,
2
{
4
,
2
,
4
}
{\displaystyle t_{0,2} \{4,2,4\}}
Bicantellated
t
1
,
3
{
4
,
2
,
4
}
{\displaystyle t_{1,3} \{4,2,4\}}
Cantitruncated
t
0
,
1
,
2
{
4
,
2
,
4
}
{\displaystyle t_{0,1,2} \{4,2,4\}}
Bicantitruncated
t
1
,
2
,
3
{
4
,
2
,
4
}
{\displaystyle t_{1,2,3} \{4,2,4\}}
Runcinated
t
0
,
3
{
4
,
2
,
4
}
{\displaystyle t_{0,3} \{4,2,4\}}
Runcicantellated
t
0
,
2
,
3
{
4
,
2
,
4
}
{\displaystyle t_{0,2,3} \{4,2,4\}}
Runcitruncated
t
0
,
1
,
3
{
4
,
2
,
4
}
{\displaystyle t_{0,1,3} \{4,2,4\}}
Runcicantitruncated
t
0
,
1
,
2
,
3
{
4
,
2
,
4
}
{\displaystyle t_{0,1,2,3} \{4,2,4\}}
Tesseract
Tesseract
Square-octagonal duoprism
Square-octagonal duoprism
Tesseract
Square-octagonal duoprism
Square-octagonal duoprism
Octagonal duoprism
Regular
t
0
{
4
,
2
,
2
}
{\displaystyle t_0 \{4,2,2\}}
Rectified
t
1
{
4
,
2
,
2
}
{\displaystyle t_1 \{4,2,2\}}
Birectified
t
2
{
4
,
2
,
2
}
{\displaystyle t_2 \{4,2,2\}}
Trirectified
t
3
{
4
,
2
,
2
}
{\displaystyle t_3 \{4,2,2\}}
Truncated
t
0
,
1
{
4
,
2
,
2
}
{\displaystyle t_{0,1} \{4,2,2\}}
Bitruncated
t
1
,
2
{
4
,
2
,
2
}
{\displaystyle t_{1,2} \{4,2,2\}}
Tritruncated
t
2
,
3
{
4
,
2
,
2
}
{\displaystyle t_{2,3} \{4,2,2\}}
Square dihedral dichoron
Rectified square dihedral dichoron
Rectified square hosohedral hosochoron
Square hosohedral hosochoron
Truncated square dihedral dichoron
Square dihedral prism
Square hosohedral prism
Cantellated
t
0
,
2
{
4
,
2
,
2
}
{\displaystyle t_{0,2} \{4,2,2\}}
Bicantellated
t
1
,
3
{
4
,
2
,
2
}
{\displaystyle t_{1,3} \{4,2,2\}}
Cantitruncated
t
0
,
1
,
2
{
4
,
2
,
2
}
{\displaystyle t_{0,1,2} \{4,2,2\}}
Bicantitruncated
t
1
,
2
,
3
{
4
,
2
,
2
}
{\displaystyle t_{1,2,3} \{4,2,2\}}
Runcinated
t
0
,
3
{
4
,
2
,
2
}
{\displaystyle t_{0,3} \{4,2,2\}}
Runcicantellated
t
0
,
2
,
3
{
4
,
2
,
2
}
{\displaystyle t_{0,2,3} \{4,2,2\}}
Runcitruncated
t
0
,
1
,
3
{
4
,
2
,
2
}
{\displaystyle t_{0,1,3} \{4,2,2\}}
Runcicantitruncated
t
0
,
1
,
2
,
3
{
4
,
2
,
2
}
{\displaystyle t_{0,1,2,3} \{4,2,2\}}
Square dihedral prism
Square dihedral prism
Truncated square dihedral prism
Tesseract
Square dihedral prism
Tesseract
Truncated square dihedral prism
Square-octagonal duoprism
Regular
t
0
{
2
,
2
,
2
}
{\displaystyle t_0 \{2,2,2\}}
Rectified
t
1
{
2
,
2
,
2
}
{\displaystyle t_1 \{2,2,2\}}
Birectified
t
2
{
2
,
2
,
2
}
{\displaystyle t_2 \{2,2,2\}}
Trirectified
t
3
{
2
,
2
,
2
}
{\displaystyle t_3 \{2,2,2\}}
Truncated
t
0
,
1
{
2
,
2
,
2
}
{\displaystyle t_{0,1} \{2,2,2\}}
Bitruncated
t
1
,
2
{
2
,
2
,
2
}
{\displaystyle t_{1,2} \{2,2,2\}}
Tritruncated
t
2
,
3
{
2
,
2
,
2
}
{\displaystyle t_{2,3} \{2,2,2\}}
Digonal dihedral dichoron
Digonal dihedral dichoron
Digonal dihedral dichoron
Digonal dihedral dichoron
Digonal dihedral prism
Digonal dihedral prism
Digonal dihedral prism
Cantellated
t
0
,
2
{
2
,
2
,
2
}
{\displaystyle t_{0,2} \{2,2,2\}}
Bicantellated
t
1
,
3
{
2
,
2
,
2
}
{\displaystyle t_{1,3} \{2,2,2\}}
Cantitruncated
t
0
,
1
,
2
{
2
,
2
,
2
}
{\displaystyle t_{0,1,2} \{2,2,2\}}
Bicantitruncated
t
1
,
2
,
3
{
2
,
2
,
2
}
{\displaystyle t_{1,2,3} \{2,2,2\}}
Runcinated
t
0
,
3
{
2
,
2
,
2
}
{\displaystyle t_{0,3} \{2,2,2\}}
Runcicantellated
t
0
,
2
,
3
{
2
,
2
,
2
}
{\displaystyle t_{0,2,3} \{2,2,2\}}
Runcitruncated
t
0
,
1
,
3
{
2
,
2
,
2
}
{\displaystyle t_{0,1,3} \{2,2,2\}}
Runcicantitruncated
t
0
,
1
,
2
,
3
{
2
,
2
,
2
}
{\displaystyle t_{0,1,2,3} \{2,2,2\}}
Digonal dihedral prism
Digonal dihedral prism
Digonal-square duoprism
Digonal-square duoprism
Digonal dihedral prism
Digonal-square duoprism
Digonal-square duoprism
Tesseract
