This folder is a related collection in this repository, not a 4-polytope
category. The models are strict orthographic 3D projections of the
Gosset-family and adjacent D/E root polytopes: 5-, 6-, 7-, 8-, 9-, and
10-orthoplexes; 5-, 6-, 7-, and 10-demicubes; rectified 5-orthoplex
(t1 2_11); E6 root polytope (1_22); 2_21, 3_21, 2_31,
1_32, 4_21, 2_41, and 1_42.
The 113 .vZome files are organized in per-source subfolders for
sharing and spot checking. “Balls” counts distinct 3D ball positions in the projected vZome
model; some vertices of the original source polytope may coincide in 3D.
Open the viewer index here:
| File | Source polytope | Balls | Symmetry |
|---|---|---|---|
2_11/2_11_B3_7_balls.vZome |
5-orthoplex (2_11) |
7 | B3-symmetric |
2_11/2_11_D4_7_balls.vZome |
5-orthoplex (2_11) |
7 | D4-symmetric |
2_11/2_11_B3_9_balls.vZome |
5-orthoplex (2_11) |
9 | B3-symmetric |
rectified_5_orthoplex/rectified_5_orthoplex_B3_19_balls.vZome |
Rectified 5-orthoplex (t1 2_11) |
19 | B3-symmetric |
rectified_5_orthoplex/rectified_5_orthoplex_D4_21_balls.vZome |
Rectified 5-orthoplex (t1 2_11) |
21 | D4-symmetric |
rectified_5_orthoplex/rectified_5_orthoplex_B3_26_balls.vZome |
Rectified 5-orthoplex (t1 2_11) |
26 | B3-symmetric |
1_21/1_21_B3_8_balls.vZome |
5-demicube (1_21) |
8 | B3-symmetric |
1_21/1_21_D4_12_balls.vZome |
5-demicube (1_21) |
12 | D4-symmetric |
1_21/1_21_B3_15_balls.vZome |
5-demicube (1_21) |
15 | B3-symmetric |
3_11/3_11_B3_6_balls.vZome |
6-orthoplex (3_11) |
6 | B3-symmetric |
3_11/3_11_D4_7_balls.vZome |
6-orthoplex (3_11) |
7 | D4-symmetric |
3_11/3_11_B3_7_balls.vZome |
6-orthoplex (3_11) |
7 | B3-symmetric |
3_11/3_11_B3_9_balls.vZome |
6-orthoplex (3_11) |
9 | B3-symmetric |
3_11/3_11_Th_12_balls.vZome |
6-orthoplex (3_11) |
12 | Th-symmetric |
3_11/3_11_H3_12_balls.vZome |
6-orthoplex (3_11) |
12 | H3-symmetric |
1_31/1_31_D4_12_balls.vZome |
6-demicube (1_31) |
12 | D4-symmetric |
1_31/1_31_B3_13_balls.vZome |
6-demicube (1_31) |
13 | B3-symmetric |
1_31/1_31_B3_14_balls.vZome |
6-demicube (1_31) |
14 | B3-symmetric |
1_31/1_31_B3_15_balls.vZome |
6-demicube (1_31) |
15 | B3-symmetric |
1_31/1_31_Th_32_balls_a.vZome |
6-demicube (1_31) |
32 | Th-symmetric |
1_31/1_31_H3_32_balls_a.vZome |
6-demicube (1_31) |
32 | H3-symmetric |
1_31/1_31_Th_32_balls_b.vZome |
6-demicube (1_31) |
32 | Th-symmetric |
1_31/1_31_H3_32_balls_b.vZome |
6-demicube (1_31) |
32 | H3-symmetric |
1_31/1_31_B3_8_balls.vZome |
6-demicube (1_31) |
8 | B3-symmetric |
2_21/2_21_B3_15_balls.vZome |
2_21 |
15 | B3-symmetric |
2_21/2_21_B3_19_balls.vZome |
2_21 |
19 | B3-symmetric |
1_22/1_22_B3_27_balls.vZome |
1_22 |
27 | B3-symmetric |
1_22/1_22_B3_33_balls.vZome |
1_22 |
33 | B3-symmetric |
4_11/4_11_D4_7_balls.vZome |
7-orthoplex (4_11) |
7 | D4-symmetric |
4_11/4_11_B3_7_balls.vZome |
7-orthoplex (4_11) |
7 | B3-symmetric |
4_11/4_11_B3_9_balls.vZome |
7-orthoplex (4_11) |
9 | B3-symmetric |
4_11/4_11_H3_13_balls.vZome |
7-orthoplex (4_11) |
13 | H3-symmetric |
4_11/4_11_Th_13_balls.vZome |
7-orthoplex (4_11) |
13 | Th-symmetric |
1_41/1_41_B3_8_balls.vZome |
7-demicube (1_41) |
8 | B3-symmetric |
1_41/1_41_D4_12_balls.vZome |
7-demicube (1_41) |
12 | D4-symmetric |
1_41/1_41_B3_15_balls.vZome |
7-demicube (1_41) |
15 | B3-symmetric |
1_41/1_41_B3_27_balls.vZome |
7-demicube (1_41) |
27 | B3-symmetric |
1_41/1_41_Th_64_balls.vZome |
7-demicube (1_41) |
64 | Th-symmetric |
1_41/1_41_H3_64_balls.vZome |
7-demicube (1_41) |
64 | H3-symmetric |
3_21/3_21_B3_14_balls.vZome |
3_21 |
14 | B3-symmetric |
3_21/3_21_B3_15_balls.vZome |
3_21 |
15 | B3-symmetric |
3_21/3_21_B3_19_balls.vZome |
3_21 |
19 | B3-symmetric |
3_21/3_21_H3_44_balls_icosa_hull.vZome |
3_21 |
44 | H3-symmetric |
3_21/3_21_H3_44_balls_dodeca_hull.vZome |
3_21 |
44 | H3-symmetric |
2_31/2_31_B3_19_balls.vZome |
2_31 |
19 | B3-symmetric |
2_31/2_31_B3_27_balls.vZome |
2_31 |
27 | B3-symmetric |
2_31/2_31_B3_33_balls.vZome |
2_31 |
33 | B3-symmetric |
2_31/2_31_H3_93_balls_hull42.vZome |
2_31 |
93 | H3-symmetric |
2_31/2_31_H3_93_balls_hull30.vZome |
2_31 |
93 | H3-symmetric |
1_32/1_32_B3_38_balls.vZome |
1_32 |
38 | B3-symmetric |
1_32/1_32_B3_59_balls.vZome |
1_32 |
59 | B3-symmetric |
1_32/1_32_B3_81_balls.vZome |
1_32 |
81 | B3-symmetric |
1_32/1_32_H3_384_balls_hull32.vZome |
1_32 |
384 | H3-symmetric |
1_32/1_32_H3_384_balls_hull80.vZome |
1_32 |
384 | H3-symmetric |
5_11/5_11_B3_7_balls.vZome |
8-orthoplex (5_11) |
7 | B3-symmetric, R=3 confirmed |
5_11/5_11_B3_8_balls.vZome |
8-orthoplex (5_11) |
8 | B3-symmetric, R=3 confirmed |
5_11/5_11_B3_9_balls.vZome |
8-orthoplex (5_11) |
9 | B3-symmetric, R=3 confirmed |
5_11/5_11_D2h_8_balls.vZome |
8-orthoplex (5_11) |
8 | D2h-symmetric, R=3 confirmed |
5_11/5_11_D2h_12_balls_a.vZome |
8-orthoplex (5_11) |
12 | D2h-symmetric, variant a, R=3 confirmed |
5_11/5_11_D2h_12_balls_b.vZome |
8-orthoplex (5_11) |
12 | D2h-symmetric, variant b, R=3 confirmed |
5_11/5_11_D3d_8_balls.vZome |
8-orthoplex (5_11) |
8 | D3d-symmetric, R=3 confirmed |
5_11/5_11_D3d_14_balls_a.vZome |
8-orthoplex (5_11) |
14 | D3d-symmetric, variant a, R=3 confirmed |
5_11/5_11_D3d_14_balls_b.vZome |
8-orthoplex (5_11) |
14 | D3d-symmetric, variant b, R=3 confirmed |
5_11/5_11_D3d_14_balls_c.vZome |
8-orthoplex (5_11) |
14 | D3d-symmetric, variant c, R=3 confirmed |
5_11/5_11_D3d_16_balls.vZome |
8-orthoplex (5_11) |
16 | D3d-symmetric, R=3 confirmed |
5_11/5_11_D4_6_balls.vZome |
8-orthoplex (5_11) |
6 | D4-symmetric, R=3 confirmed |
5_11/5_11_D4_7_balls.vZome |
8-orthoplex (5_11) |
7 | D4-symmetric, R=3 confirmed |
5_11/5_11_D4_10_balls.vZome |
8-orthoplex (5_11) |
10 | D4-symmetric, R=3 confirmed |
5_11/5_11_D5d_14_balls_a.vZome |
8-orthoplex (5_11) |
14 | D5d-symmetric, variant a, R=3 confirmed |
5_11/5_11_D5d_14_balls_b.vZome |
8-orthoplex (5_11) |
14 | D5d-symmetric, variant b, R=3 confirmed |
5_11/5_11_H3_13_balls.vZome |
8-orthoplex (5_11) |
13 | H3-symmetric, R=3 confirmed |
5_11/5_11_Th_13_balls.vZome |
8-orthoplex (5_11) |
13 | Th-symmetric, R=3 confirmed |
4_21/4_21_B3_27_balls.vZome |
4_21 |
27 | B3-symmetric |
4_21/4_21_B3_33_balls.vZome |
4_21 |
33 | B3-symmetric |
4_21/4_21_H3_137_balls.vZome |
4_21 |
137 | H3-symmetric |
2_41/2_41_B3_65_balls.vZome |
2_41 |
65 | B3-symmetric |
2_41/2_41_B3_93_balls.vZome |
2_41 |
93 | B3-symmetric |
2_41/2_41_H3_921_balls.vZome |
2_41 |
921 | H3-symmetric |
1_42/1_42_B3_169_balls.vZome |
1_42 |
169 | B3-symmetric |
1_42/1_42_B3_251_balls.vZome |
1_42 |
251 | B3-symmetric |
1_42/1_42_H3_5936_balls.vZome |
1_42 |
5936 | H3-symmetric |
6_11/6_11_B3_6_balls.vZome |
9-orthoplex (6_11) |
6 | B3-symmetric |
6_11/6_11_B3_7_balls.vZome |
9-orthoplex (6_11) |
7 | B3-symmetric |
6_11/6_11_B3_9_balls.vZome |
9-orthoplex (6_11) |
9 | B3-symmetric |
6_11/6_11_D2h_13_balls.vZome |
9-orthoplex (6_11) |
13 | D2h-symmetric |
6_11/6_11_D3d_15_balls.vZome |
9-orthoplex (6_11) |
15 | D3d-symmetric |
6_11/6_11_D4_7_balls.vZome |
9-orthoplex (6_11) |
7 | D4-symmetric |
6_11/6_11_H3_13_balls.vZome |
9-orthoplex (6_11) |
13 | H3-symmetric |
6_11/6_11_Th_13_balls.vZome |
9-orthoplex (6_11) |
13 | Th-symmetric |
7_11/7_11_D4_7_balls.vZome |
10-orthoplex (7_11) |
7 | D4-symmetric |
7_11/7_11_B3_7_balls.vZome |
10-orthoplex (7_11) |
7 | B3-symmetric |
7_11/7_11_B3_9_balls.vZome |
10-orthoplex (7_11) |
9 | B3-symmetric |
7_11/7_11_H3_13_balls.vZome |
10-orthoplex (7_11) |
13 | H3-symmetric |
7_11/7_11_D2h_13_balls.vZome |
10-orthoplex (7_11) |
13 | D2h-symmetric |
7_11/7_11_Th_13_balls.vZome |
10-orthoplex (7_11) |
13 | Th-symmetric |
7_11/7_11_C3i_14_balls.vZome |
10-orthoplex (7_11) |
14 | C3i-symmetric |
7_11/7_11_D3d_15_balls.vZome |
10-orthoplex (7_11) |
15 | D3d-symmetric |
7_11/7_11_H3_20_balls.vZome |
10-orthoplex (7_11) |
20 | H3-symmetric |
1_71/1_71_B3_8_balls.vZome |
10-demicube (1_71) |
8 | B3-symmetric |
1_71/1_71_D4_12_balls.vZome |
10-demicube (1_71) |
12 | D4-symmetric |
1_71/1_71_B3_15_balls.vZome |
10-demicube (1_71) |
15 | B3-symmetric |
1_71/1_71_B3_27_balls.vZome |
10-demicube (1_71) |
27 | B3-symmetric |
1_71/1_71_D4_45_balls.vZome |
10-demicube (1_71) |
45 | D4-symmetric |
1_71/1_71_Th_64_balls.vZome |
10-demicube (1_71) |
64 | Th-symmetric |
1_71/1_71_B3_64_balls.vZome |
10-demicube (1_71) |
64 | B3-symmetric |
1_71/1_71_H3_64_balls.vZome |
10-demicube (1_71) |
64 | H3-symmetric |
1_71/1_71_B3_65_balls.vZome |
10-demicube (1_71) |
65 | B3-symmetric |
1_71/1_71_D2h_144_balls.vZome |
10-demicube (1_71) |
144 | D2h-symmetric |
1_71/1_71_D3d_161_balls.vZome |
10-demicube (1_71) |
161 | D3d-symmetric |
1_71/1_71_C3i_184_balls_a.vZome |
10-demicube (1_71) |
184 | C3i-symmetric |
1_71/1_71_C3i_184_balls_b.vZome |
10-demicube (1_71) |
184 | C3i-symmetric, variant b |
1_71/1_71_H3_364_balls_a.vZome |
10-demicube (1_71) |
364 | H3-symmetric |
1_71/1_71_H3_364_balls_b.vZome |
10-demicube (1_71) |
364 | H3-symmetric, variant b |
The symmetry labels are full Euclidean point-cloud symmetries: B3 means full
octahedral symmetry (order 48), D4 means full tetragonal/dihedral symmetry
(order 16), Th means tetrahedral symmetry with inversion (order 24), H3 means
full icosahedral symmetry (order 120), and D5d means full pentagonal
antiprismatic/dihedral symmetry (order 20). Lower-symmetry labels D2h, C3i,
and D3d are used where applicable. See symmetry_analysis.json
and the per-source manifests.
These models were found by raw-column Z[phi]^3 sweeps and exact
post-processing audits. For the 8-orthoplex (5_11), R=3 matched the R=2
set exactly with the 18 models listed here. For the 9-orthoplex (6_11), R=2 confirmed all 8 R=1 models and
found no new signatures. For the 10-orthoplex (7_11), R=2 also matched R=1
with the same nine models. The 10-demicube (1_71) R=2 check likewise
matched R=1 for its 13 direct even-coset models, with C3i and H3 variant pairs
included as separate labelled models. Earlier D/E-source saturation notes are
recorded in ../../docs/GOSSET_PROJECTIONS.md.