Tesseract and 16-cell faces

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This list shows the k-faces of the tesseract and its dual 16-cell.

Tesseract k-faces with labels from −40 to 40
Tesseract vertices with labels from 0 to 15

Searching first by weight and then by pattern gives a meaningful order.
Both terms refer to the non-zero entries of the balanced ternary vector on the left.
These vectors are the coordinate vectors of the face centers of the tesseract. (Compare example for the cube.)
A map from faces (−40 to 40) to tesseract vertices (0 to 15) can be found here.

index b. t.
vector
pattern weight tesseract
face type
tesseract
vertices
tesseract
image
16-cell
face type
16-cell
image
−40 Vector −−−−.svg 15
!!!!
4 t 0
vertex
0 c 3
tetrahedron
4 spheres, cell 00, hollow.png
−39 Vector 0−−−.svg 14
.!!!
3 t 1
edge
0, 1 c 2
triangle
4 spheres, triangle 00 01.png
−38 Vector +−−−.svg 15
!!!!
4 t 0
vertex
1 c 3
tetrahedron
4 spheres, cell 01, hollow.png
−37 Vector −0−−.svg 13
!.!!
3 t 1
edge
0, 2 c 2
triangle
4 spheres, triangle 00 02.png
−36 Vector 00−−.svg 12
..!!
2 t 2
square
0, 1, 2, 3 Tesseract square 00.png c 1
edge
4 spheres, dashed edge 0 1 - ex2 ex3.png
−35 Vector +0−−.svg 13
!.!!
3 t 1
edge
1, 3 c 2
triangle
4 spheres, triangle 01 03.png
−34 Vector −+−−.svg 15
!!!!
4 t 0
vertex
2 c 3
tetrahedron
4 spheres, cell 02, hollow.png
−33 Vector 0+−−.svg 14
.!!!
3 t 1
edge
2, 3 c 2
triangle
4 spheres, triangle 02 03.png
−32 Vector ++−−.svg 15
!!!!
4 t 0
vertex
3 c 3
tetrahedron
4 spheres, cell 03, hollow.png
−31 Vector −−0−.svg 11
!!.!
3 t 1
edge
0, 4 c 2
triangle
4 spheres, triangle 00 04.png
−30 Vector 0−0−.svg 10
.!.!
2 t 2
square
0, 1, 4, 5 Tesseract square 01.png c 1
edge
4 spheres, dashed edge 0 2 - ex1 ex3.png
−29 Vector +−0−.svg 11
!!.!
3 t 1
edge
1, 5 c 2
triangle
4 spheres, triangle 01 05.png
−28 Vector −00−.svg 9
!..!
2 t 2
square
0, 2, 4, 6 Tesseract square 02.png c 1
edge
4 spheres, dashed edge 1 2 - ex0 ex3.png
−27 Vector 000−.svg 8
...!
1 t 3
cube
0, 1, 2, 3,
4, 5, 6, 7
Tesseract cube 0.png c 0
vertex
4 spheres, vertex ex3.png
−26 Vector +00−.svg 9
!..!
2 t 2
square
1, 3, 5, 7 Tesseract square 03.png c 1
edge
4 spheres, dashed edge 1 2 - in0 ex3.png
−25 Vector −+0−.svg 11
!!.!
3 t 1
edge
2, 6 c 2
triangle
4 spheres, triangle 02 06.png
−24 Vector 0+0−.svg 10
.!.!
2 t 2
square
2, 3, 6, 7 Tesseract square 04.png c 1
edge
4 spheres, dashed edge 0 2 - in1 ex3.png
−23 Vector ++0−.svg 11
!!.!
3 t 1
edge
3, 7 c 2
triangle
4 spheres, triangle 03 07.png
−22 Vector −−+−.svg 15
!!!!
4 t 0
vertex
4 c 3
tetrahedron
4 spheres, cell 04, hollow.png
−21 Vector 0−+−.svg 14
.!!!
3 t 1
edge
4, 5 c 2
triangle
4 spheres, triangle 04 05.png
−20 Vector +−+−.svg 15
!!!!
4 t 0
vertex
5 c 3
tetrahedron
4 spheres, cell 05, hollow.png
−19 Vector −0+−.svg 13
!.!!
3 t 1
edge
4, 6 c 2
triangle
4 spheres, triangle 04 06.png
−18 Vector 00+−.svg 12
..!!
2 t 2
square
4, 5, 6, 7 Tesseract square 05.png c 1
edge
4 spheres, dashed edge 0 1 - in2 ex3.png
−17 Vector +0+−.svg 13
!.!!
3 t 1
edge
5, 7 c 2
triangle
4 spheres, triangle 05 07.png
−16 Vector −++−.svg 15
!!!!
4 t 0
vertex
6 c 3
tetrahedron
4 spheres, cell 06, hollow.png
−15 Vector 0++−.svg 14
.!!!
3 t 1
edge
6, 7 c 2
triangle
4 spheres, triangle 06 07.png
−14 Vector +++−.svg 15
!!!!
4 t 0
vertex
7 c 3
tetrahedron
4 spheres, cell 07, hollow.png
−13 Vector −−−0.svg 7
!!!.
3 t 1
edge
0, 8 c 2
triangle
4 spheres, triangle 00 08.png
−12 Vector 0−−0.svg 6
.!!.
2 t 2
square
0, 1, 8, 9 Tesseract square 06.png c 1
edge
4 spheres, dashed edge 0 3 - ex1 ex2.png
−11 Vector +−−0.svg 7
!!!.
3 t 1
edge
1, 9 c 2
triangle
4 spheres, triangle 01 09.png
−10 Vector −0−0.svg 5
!.!.
2 t 2
square
0, 2, 8, 10 Tesseract square 07.png c 1
edge
4 spheres, dashed edge 1 3 - ex0 ex2.png
−9 Vector 00−0.svg 4
..!.
1 t 3
cube
0, 1, 2, 3,
8, 9, 10, 11
Tesseract cube 1.png c 0
vertex
4 spheres, vertex ex2.png
−8 Vector +0−0.svg 5
!.!.
2 t 2
square
1, 3, 9, 11 Tesseract square 08.png c 1
edge
4 spheres, dashed edge 1 3 - in0 ex2.png
−7 Vector −+−0.svg 7
!!!.
3 t 1
edge
2, 10 c 2
triangle
4 spheres, triangle 02 10.png
−6 Vector 0+−0.svg 6
.!!.
2 t 2
square
2, 3, 10, 11 Tesseract square 09.png c 1
edge
4 spheres, dashed edge 0 3 - in1 ex2.png
−5 Vector ++−0.svg 7
!!!.
3 t 1
edge
3, 11 c 2
triangle
4 spheres, triangle 03 11.png
−4 Vector −−00.svg 3
!!..
2 t 2
square
0, 4, 8, 12 Tesseract square 11.png c 1
edge
4 spheres, dashed edge 2 3 - ex0 ex1.png
−3 Vector 0−00.svg 2
.!..
1 t 3
cube
0, 1, 4, 5,
8, 9, 12, 13
Tesseract cube 2.png c 0
vertex
4 spheres, vertex ex1.png
−2 Vector +−00.svg 3
!!..
2 t 2
square
1, 5, 9, 13 Tesseract square 12.png c 1
edge
4 spheres, dashed edge 2 3 - in0 ex1.png
−1 Vector −000.svg 1
!...
1 t 3
cube
0, 2, 4, 6,
8, 10, 12, 14
Tesseract cube 3.png c 0
vertex
4 spheres, vertex ex0.png
0 Vector 0000.svg 0
....
0 t 4
tesseract
0 ... 15 Tesseract Schlegel numbered.png c 4
16-cell
1 Vector +000.svg 1
!...
1 t 3
cube
1, 3, 5, 7,
9, 11, 13, 15
Tesseract cube 4.png c 0
vertex
4 spheres, vertex in0.png
2 Vector −+00.svg 3
!!..
2 t 2
square
2, 6, 10, 14 Tesseract square 15.png c 1
edge
4 spheres, dashed edge 2 3 - ex0 in1.png
3 Vector 0+00.svg 2
.!..
1 t 3
cube
2, 3, 6, 7,
10, 11, 14, 15
Tesseract cube 5.png c 0
vertex
4 spheres, vertex in1.png
4 Vector ++00.svg 3
!!..
2 t 2
square
3, 7, 11, 15 Tesseract square 18.png c 1
edge
4 spheres, dashed edge 2 3 - in0 in1.png
5 Vector −−+0.svg 7
!!!.
3 t 1
edge
4, 12 c 2
triangle
4 spheres, triangle 04 12.png
6 Vector 0−+0.svg 6
.!!.
2 t 2
square
4, 5, 12, 13 Tesseract square 13.png c 1
edge
4 spheres, dashed edge 0 3 - ex1 in2.png
7 Vector +−+0.svg 7
!!!.
3 t 1
edge
5, 13 c 2
triangle
4 spheres, triangle 05 13.png
8 Vector −0+0.svg 5
!.!.
2 t 2
square
4, 6, 12, 14 Tesseract square 16.png c 1
edge
4 spheres, dashed edge 1 3 - ex0 in2.png
9 Vector 00+0.svg 4
..!.
1 t 3
cube
4, 5, 6, 7,
12, 13, 14, 15
Tesseract cube 6.png c 0
vertex
4 spheres, vertex in2.png
10 Vector +0+0.svg 5
!.!.
2 t 2
square
5, 7, 13, 15 Tesseract square 19.png c 1
edge
4 spheres, dashed edge 1 3 - in0 in2.png
11 Vector −++0.svg 7
!!!.
3 t 1
edge
6, 14 c 2
triangle
4 spheres, triangle 06 14.png
12 Vector 0++0.svg 6
.!!.
2 t 2
square
6, 7, 14, 15 Tesseract square 21.png c 1
edge
4 spheres, dashed edge 0 3 - in1 in2.png
13 Vector +++0.svg 7
!!!.
3 t 1
edge
7, 15 c 2
triangle
4 spheres, triangle 07 15.png
14 Vector −−−+.svg 15
!!!!
4 t 0
vertex
8 c 3
tetrahedron
4 spheres, cell 08, hollow.png
15 Vector 0−−+.svg 14
.!!!
3 t 1
edge
8, 9 c 2
triangle
4 spheres, triangle 08 09.png
16 Vector +−−+.svg 15
!!!!
4 t 0
vertex
9 c 3
tetrahedron
4 spheres, cell 09, hollow.png
17 Vector −0−+.svg 13
!.!!
3 t 1
edge
8, 10 c 2
triangle
4 spheres, triangle 08 10.png
18 Vector 00−+.svg 12
..!!
2 t 2
square
8, 9, 10, 11 Tesseract square 10.png c 1
edge
4 spheres, dashed edge 0 1 - ex2 in3.png
19 Vector +0−+.svg 13
!.!!
3 t 1
edge
9, 11 c 2
triangle
4 spheres, triangle 09 11.png
20 Vector −+−+.svg 15
!!!!
4 t 0
vertex
10 c 3
tetrahedron
4 spheres, cell 10, hollow.png
21 Vector 0+−+.svg 14
.!!!
3 t 1
edge
10, 11 c 2
triangle
4 spheres, triangle 10 11.png
22 Vector ++−+.svg 15
!!!!
4 t 0
vertex
11 c 3
tetrahedron
4 spheres, cell 11, hollow.png
23 Vector −−0+.svg 11
!!.!
3 t 1
edge
8, 12 c 2
triangle
4 spheres, triangle 08 12.png
24 Vector 0−0+.svg 10
.!.!
2 t 2
square
8, 9, 12, 13 Tesseract square 14.png c 1
edge
4 spheres, dashed edge 0 2 - ex1 in3.png
25 Vector +−0+.svg 11
!!.!
3 t 1
edge
9, 13 c 2
triangle
4 spheres, triangle 09 13.png
26 Vector −00+.svg 9
!..!
2 t 2
square
8, 10, 12, 14 Tesseract square 17.png c 1
edge
4 spheres, dashed edge 1 2 - ex0 in3.png
27 Vector 000+.svg 8
...!
1 t 3
cube
8, 9, 10, 11,
12, 13, 14, 15
Tesseract cube 7.png c 0
vertex
4 spheres, vertex in3.png
28 Vector +00+.svg 9
!..!
2 t 2
square
9, 11, 13, 15 Tesseract square 20.png c 1
edge
4 spheres, dashed edge 1 2 - in0 in3.png
29 Vector −+0+.svg 11
!!.!
3 t 1
edge
10, 14 c 2
triangle
4 spheres, triangle 10 14.png
30 Vector 0+0+.svg 10
.!.!
2 t 2
square
10, 11, 14, 15 Tesseract square 22.png c 1
edge
4 spheres, dashed edge 0 2 - in1 in3.png
31 Vector ++0+.svg 11
!!.!
3 t 1
edge
11, 15 c 2
triangle
4 spheres, triangle 11 15.png
32 Vector −−++.svg 15
!!!!
4 t 0
vertex
12 c 3
tetrahedron
4 spheres, cell 12, hollow.png
33 Vector 0−++.svg 14
.!!!
3 t 1
edge
12, 13 c 2
triangle
4 spheres, triangle 12 13.png
34 Vector +−++.svg 15
!!!!
4 t 0
vertex
13 c 3
tetrahedron
4 spheres, cell 13, hollow.png
35 Vector −0++.svg 13
!.!!
3 t 1
edge
12, 14 c 2
triangle
4 spheres, triangle 12 14.png
36 Vector 00++.svg 12
..!!
2 t 2
square
12, 13, 14, 15 Tesseract square 23.png c 1
edge
4 spheres, dashed edge 0 1 - in2 in3.png
37 Vector +0++.svg 13
!.!!
3 t 1
edge
13, 15 c 2
triangle
4 spheres, triangle 13 15.png
38 Vector −+++.svg 15
!!!!
4 t 0
vertex
14 c 3
tetrahedron
4 spheres, cell 14, hollow.png
39 Vector 0+++.svg 14
.!!!
3 t 1
edge
14, 15 c 2
triangle
4 spheres, triangle 14 15.png
40 Vector ++++.svg 15
!!!!
4 t 0
vertex
15 c 3
tetrahedron
4 spheres, cell 15, hollow.png