Swirlchoron

A swirlchoron is a polychoron that expresses the Hopf fibration of a given polyhedron. In other words, the vertices or cells of a polychoron map to a ring of swirling great circles within a glome that represents a face of a polytwister, and are therefore their polychoric approximations. For every regular spherical polyhedron (including degenerate dihedra/hosohedra), a swirlchoron can be constructed. Their vertices can be compounded to form new swirlchora, an example being the 1-bitetrahedral swirlprism, being the compound of two hexadecachora in tetrahedral swirlprism symmetry, or the tri-icositetradiminished hexacosichoron, being the tetragonal-antiwedge compound of two icositetrachora in cubic swirlprism symmetry.

Swirlchora can be isogonal or isochoric. Some swirlchora, such as the bi-icositetradiminished hexacosichoron and its dual, the tri-icositetradiminished hexacosichoron, are both isogonal and isochoric, and are therefore noble.

Octahedron-based isogonal swirlprisms
Coordinates for the vertices of a 4n-fold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations and sign changes of: defining an icositetrachoron, along with reflections through the x=y and z=w hyperplanes ({x,y,z,w} = {z,w,x,y} = {y,x,w,z} = {w,z,y,x}) and with all sign changes of (k represents any number from 1 up to floor(n/2)): along with reflections through the x=y and z=w hyperplanes and with all even sign changes of (if n is odd, then k represents any odd number from 1 up to n; if n is even, then k represents any number from 0 up to n/2): along with reflections through the x=y and z=w hyperplanes and with all odd sign changes of:
 * (0, 0, 0, 1),
 * (1/2, 1/2, 1/2, 1/2),
 * (0, 0, cos(kπ/2n), sin(kπ/2n)),
 * (sin(kπ/4n)/$\sqrt{2}$, cos(kπ/4n)/$\sqrt{2}$, sin(kπ/4n)/$\sqrt{2}$, cos(kπ/4n)/$\sqrt{2}$) (if n is odd),
 * (sin(kπ/2n)/$\sqrt{2}$, cos(kπ/2n)/$\sqrt{2}$, sin(kπ/2n)/$\sqrt{2}$, cos(kπ/2n)/$\sqrt{2}$) (if n is even),
 * (sin(kπ/4n)/$\sqrt{2}$, cos(kπ/4n)/$\sqrt{2}$, cos(kπ/4n)/$\sqrt{2}$, sin(kπ/4n)/$\sqrt{2}$) (if n is odd),
 * (sin(kπ/2n)/$\sqrt{2}$, cos(kπ/2n)/$\sqrt{2}$, cos(kπ/2n)/$\sqrt{2}$, sin(kπ/2n)/$\sqrt{2}$) (if n is even).

Tetrahedron-based
1. Hexadecachoron (8 vertices, octahedron vertex figure) - tesseract (16 cubes)

2. Tetrafold tetraswirlchoron (16 vertices, triakis triangular bipyramid vertex figure) - tetraswirlic hexadecachoron or tetswirl 16 (16 truncated triangular prisms)

3. Icositetrachoron (24 vertices, cube vertex figure) - dual icositetrahedron (24 octahedra)

4. Octafold tetraswirlchoron (32 vertices, vertical-bisected joined triangular prism vertex figure) - tetraswirlic triacontadichoron or tetswirl 32 (96 edge-alternate laterostellated hexagonal prisms)

5. Decafold tetraswirlchoron (40 vertices, alternate-metatriakis hexagonal bipyramid vertex figure) - tetraswirlic tetracontachoron or tetswirl 40 (40 alternate-metatruncated hexagonal prisms)

6. Dodecafold tetraswirlchoron (48 vertices, edge-vertical bisected trigonal trapezohedron vertex figure) - tetraswirlic tetracontoctachoron or tetswirl 48 (48 rhombistellated hexagonal antiprisms)

7. Tetradecafold tetraswirlchoron (56 vertices) - tetraswirlic pentacontahexachoron or tetswirl 56 (56 cells)

8. Hexadecafold tetraswirlchoron (64 vertices) - tetraswirlic hexacontatetrachoron or tetswirl 64 (64 cells)

9. Octadecafold tetraswirlchoron (72 vertices) - tetraswirlic heptacontadichoron or tetswirl 72 (72 cells)

10. Icosafold tetraswirlchoron (80 vertices) - tetraswirlic octacontachoron or tetswirl 80 (80 cells)

Small rhombitetratetrahedron-based
1. Small tetrafold rhombitetraswirlchoron (48 vertices) - deltododecaswirlic tetracontoctachoron (48 cells)

2. Small dodecafold rhombitetraswirlchoron (144 vertices) - deltododecaswirlic hecatonictetracontatetrachoron (144 cells)

3. Small icosafold rhombitetraswirlchoron (240 vertices) - deltododecaswirlic diacositetracontachoron (240 cells)

4. Small icosioctafold rhombitetraswirlchoron (336 vertices) - deltododecaswirlic triacositriacontahexachoron (336 cells)

5. Small triacontahexafold rhombitetraswirlchoron (432 vertices) - deltododecaswirlic tetracositriacontadichoron (432 cells)

6. Small tetracontatetrafold rhombitetraswirlchoron (528 vertices) - deltododecaswirlic pentacosicosoctachoron (528 cells)

7. Small pentacontadifold rhombitetraswirlchoron (624 vertices) - deltododecaswirlic hexacosicositetrachoron (624 cells)

8. Small hexecontafold rhombitetraswirlchoron (720 vertices) - deltododecaswirlic heptacosiicosachoron (720 cells)

9. Small hexacontoctafold rhombitetraswirlchoron (816 vertices) - deltododecaswirlic octacosihexadecachoron (816 cells)

10. Small heptacontahexafold rhombitetraswirlchoron (912 vertices) - deltododecaswirlic enneacosidodecachoron (912 cells)

Cube-based
1. Square-antiprismatic heptacontadichoron (96 vertices, trigonal trapezohedron vertex figure) - triangular-antiprismatic enneacontahexachoron (96 triangular antiprisms)

2. Icositetrafold cubiswirlchoron (192 vertices, edge-vertical bisected trigonal trapezohedron vertex figure) - octaswirlic hecatonicenneacontadichoron or octswirl 192 (192 rhombistellated hexagonal antiprisms)

3. Triacontahexafold cubiswirlchoron (288 vertices) - octaswirlic diacosioctacontoctachoron or octswirl 288 (288 cells)

4. Tetracontoctafold cubiswirlchoron (384 vertices) - octaswirlic triacosioctacontatetrachoron or octswirl 384 (384 cells)

5. Hexecontafold cubiswirlchoron (480 vertices) - octaswirlic tetracosioctacontachoron or octswirl 480 (480 cells)

6. Heptacontadifold cubiswirlchoron (576 vertices) - octaswirlic pentacosiheptacontahexachoron or octswirl 576 (576 cells)

7. Octacontatetrafold cubiswirlchoron (672 vertices) - octaswirlic hexacosiheptacontadichoron or octswirl 672 (672 cells)

8. Enneacontahexafold cubiswirlchoron (768 vertices) - octaswirlic heptacosihexacontoctachoron or octswirl 768 (768 cells)

9. Hecatonicoctafold cubiswirlchoron (864 vertices) - octaswirlic octacosihexacontatetrachoron or octswirl 864 (864 cells)

10. Hecatonicosafold cubiswirlchoron (960 vertices) - octaswirlic enneacosihexecontachoron or octswirl 960 (960 cells)

Octahedron-based
1. Icositetrachoron (24 vertices, cube vertex figure) - dual icositetrahedron (24 octahedra)

2. Bitetracontoctachoron (48 vertices, triakis octahedron vertex figure) - tetracontoctachoron (48 truncated cubes)

3. Triangular-antiprismatic enneacontahexachoron or octswirl 96 (72 vertices, tetragonal trapezohedron vertex figure) - square-antiprismatic heptacontadichoron or cubeswirl 72 (72 square antiprisms)

4. Hexadecafold octaswirlchoron (96 vertices, bisected rhombic dodecahedron vertex figure) - cubiswirlic enneacontahexachoron or cubeswirl 96 (96 edge-alternate laterostellated octagonal prisms)

5. Icosafold octaswirlchoron (120 vertices, alternate-metatriakis octagonal bipyramid vertex figure) - cubiswirlic hecatonicosachoron or cubeswirl 120 (120 alternate-metatruncated octagonal prisms)

6. Icositetrafold octaswirlchoron (144 vertices, edge-vertical bisected tetragonal trapezohedron vertex figure) - cubiswirlic hecatonictetracontatetrachoron or cubeswirl 144 (144 rhombistellated octagonal antiprisms)

7. Icosioctafold octaswirlchoron (168 vertices) - cubiswirlic hecatonichexacontaoctachoron or cubeswirl 168 (168 cells)

8. Triacontadifold octaswirlchoron (192 vertices) - cubiswirlic hecatonicenneacontadichoron or cubeswirl 192 (192 cells)

9. Triacontahexafold octaswirlchoron (216 vertices) - cubiswirlic diacosihexadecachoron or cubeswirl 216 (216 cells)

10. Tetracontafold octaswirlchoron (240 vertices) - cubiswirlic diacositetracontachoron or cubeswirl 240 (240 cells)

Cuboctahedron-based
1. Octafold cuboctaswirlchoron (96 vertices) - rhombidodecaswirlic enneacontahexachoron (96 cells)

2. Hexadecafold cuboctaswirlchoron (192 vertices) - rhombidodecaswirlic hecatonicennacontadichoron (192 cells)

3. Icositetrafold cuboctaswirlchoron (288 vertices, rectangular trapezohedron vertex figure) - rhombidodecaswirlic diacosioctacontoctachoron (288 rhombic antiprism cells)

4. Triacontadifold cuboctaswirlchoron (384 vertices) - - rhombidodecaswirlic triacosioctacontatetrachoron (384 cells)

5. Tetracontafold cuboctaswirlchoron (480 vertices) - rhombidodecaswirlic tetracosioctacontachoron (480 cells)

6. Tetracontoctafold cuboctaswirlchoron (576 vertices) - rhombidodecaswirlic pentacosiheptacontahexachoron (576 cells)

7. Pentacontahexafold cuboctaswirlchoron (672 vertices) - rhombidodecaswirlic hexacosiheptacontadichoron (672 cells)

8. Hexacontatetrafold cuboctaswirlchoron (768 vertices) - rhombidodecaswirlic heptacosihexacontoctachoron (768 cells)

9. Heptacontadifold cuboctaswirlchoron (864 vertices) - rhombidodecaswirlic octacosihexacontatetrachoron (864 cells)

10. Octacontafold cuboctaswirlchoron (960 vertices) - rhombidodecaswirlic enneacosihexecontachoron (960 cells)

Chiral cuboctahedron-based
1. Bitetracontoctachoron (48 vertices, triakis octahedron vertex figure) - tetracontoctachoron (48 truncated cubes)

2. Chirododecafold cuboctaswirlchoron (144 vertices) - chirorhombidodecaswirlic hecatonictetracontatetrachoron (144 cells)

3. Chiroicosafold cuboctaswirlchoron (240 vertices) - chirorhombidodecaswirlic diacositetracontachoron (240 cells)

4. Chiroicosioctafold cuboctaswirlchoron (336 vertices) - chirorhombidodecaswirlic triacositriacontahexachoron (336 cells)

5. Chirotriacontahexafold cuboctaswirlchoron (432 vertices) - chirorhombidodecaswirlic tetracositriacontadichoron (432 cells)

6. Chirotetracontatetrafold cuboctaswirlchoron (528 vertices) - chirorhombidodecaswirlic pentacosicosoctachoron (528 cells)

7. Chiropentacontadifold cuboctaswirlchoron (624 vertices) - chirorhombidodecaswirlic hexacosicositetrachoron (624 cells)

8. Chirohexecontafold cuboctaswirlchoron (720 vertices) - chirorhombidodecaswirlic heptacosiicosachoron (720 cells)

9. Chirohexacontoctafold cuboctaswirlchoron (816 vertices) - chirorhombidodecaswirlic octacosihexadecachoron (816 cells)

10. Chiroheptacontahexafold cuboctaswirlchoron (912 vertices) - chirorhombidodecaswirlic enneacosidodecachoron (912 cells)

Dodecahedron-based
1. Pentagonal-antiprismatic triacosihexecontachoron (600 vertices, trigonal trapezohedron vertex figure) - triangular-antiprismatic hexacosichoron (600 triangular antiprisms)

2. Hexecontafold dodecaswirlchoron (1200 vertices, edge-vertical bisected trigonal trapezohedron vertex figure) - icosaswirlic chilliadiacosichoron or ikeswirl 1200 (1200 rhombistellated hexagonal antiprisms)

3. Enneacontafold dodecaswirlchoron (1800 vertices) - icosaswirlic chilliaoctacosichoron or ikeswirl 1800 (1800 cells)

4. Hecatonicosafold dodecaswirlchoron (2400 vertices) - icosaswirlic dischilliatetracosichoron or ikeswirl 2400 (2400 cells)

5. Hecatonicpentacontafold dodecaswirlchoron (3000 vertices) - icosaswirlic trischilliachoron or ikeswirl 3000 (3000 cells)

6. Hecatonicoctacontafold dodecaswirlchoron (3600 vertices) - icosaswirlic trischilliahexacosichoron or ikeswirl 3600 (3600 cells)

7. Diacosidecafold dodecaswirlchoron (4200 vertices) - icosaswirlic tetrachilliadiacosichoron or ikeswirl 4200 (4200 cells)

8. Diacositetracontafold dodecaswirlchoron (4800 vertices) - icosaswirlic tetrachilliaoctacosichoron or ikeswirl 4800 (4800 cells)

9. Diacosiheptacontafold dodecaswirlchoron (5400 vertices) - icosaswirlic pentachilliatetracosichoron or ikeswirl 5400 (5400 cells)

10. Triacosifold dodecaswirlchoron (6000 vertices) - icosaswirlic hexachilliachoron or ikeswirl 6000 (6000 cells)

Icosahedron-based
1. Hexacosichoron (120 vertices, icosahedron vertex figure) - hecatonicosachoron (120 dodecahedra)

2. Icosafold icosaswirlchoron (240 vertices, triakis pentagonal bipyramid vertex figure) - dodecaswirlic diacositetracontachoron or doeswirl 240 (240 truncated pentagonal prisms)

3. Triangular-antiprismatic hexacosichoron or ikeswirl 600 (360 vertices, pentagonal trapezohedron vertex figure) - pentagonal-antiprismatic triacosihexecontachoron or doeswirl 360 (360 pentagonal antiprisms)

4. Tetracontafold icosaswirlchoron (480 vertices, vertical-bisected joined pentagonal prism vertex figure) - dodecaswirlic tetracosioctacontachoron or doeswirl 480 (480 edge-alternate laterostellated decagonal prisms)

5. Pentacontafold icosaswirlchoron (600 vertices, alternate-metatriakis decagonal bipyramid vertex figure) - dodecaswirlic hexacosichoron or doeswirl 600 (600 alternate-metatruncated decagonal prisms)

6. Hexecontafold icosaswirlchoron (720 vertices, edge-vertical bisected pentagonal trapezohedron vertex figure) - dodecaswirlic heptacosiicosachoron or doeswirl 720 (720 rhombistellated decagonal antiprisms)

7. Heptacontafold icosaswirlchoron (840 vertices) - dodecaswirlic octacositetracontachoron or doeswirl 840 (840 cells)

8. Octacontafold icosaswirlchoron (960 vertices) - dodecaswirlic enneacosihexecontachoron or doeswirl 960 (960 cells)

9. Enneacontafold icosaswirlchoron (1080 vertices) - dodecaswirlic chilliaoctacontachoron or doeswirl 1080 (1080 cells)

10. Hectofold icosaswirlchoron (1200 vertices) - dodecaswirlic chilliadiacosichoron or doeswirl 1200 (1200 cells)

Icosidodecahedron-based
1. Hexacosichoron (120 vertices, icosahedron vertex figure) - hecatonicosachoron (120 dodecahedra)

2. Bitetrahedral diacositetracontachoron (240 vertices, chiral ditriakis tetrahedron vertex figure) - ditruncated-tetrahedral diacositetracontachoron (240 chiral ditruncated tetrahedra)

3. Dodecafold icosidodecaswirlchoron (360 vertices) - rhombitriacontaswirlic triacosihexecontachoron (360 cells)

4. Hexadecafold icosidodecaswirlchoron (480 vertices) - - rhombitriacontaswirlic tetracosioctacontachoron (480 cells)

5. Icosafold icosidodecaswirlchoron (600 vertices) - rhombitriacontaswirlic hexacosichoron (600 cells)

6. Icositetrafold icosidodecaswirlchoron (720 vertices) - rhombitriacontaswirlic heptacosiicosachoron (720 cells)

7. Icosioctafold icosidodecaswirlchoron (840 vertices) - rhombitriacontaswirlic octacositetracontachoron (840 cells)

8. Triacontadifold icosidodecaswirlchoron (960 vertices) - rhombitriacontaswirlic enneacosihexecontachoron (960 cells)

9. Triacontahexafold icosidodecaswirlchoron (1080 vertices) - rhombitriacontaswirlic chilliaoctacontachoron (1080 cells)

10. Tetracontafold icosidodecaswirlchoron (1200 vertices) - rhombitriacontaswirlic chilliadiacosichoron (1200 cells)

12. Tetracontoctafold icosidodecaswirlchoron (1440 vertices) - rhombitriacontaswirlic chilliatetracositetracontachoron (1440 cells)

15. Hexecontafold icosidodecaswirlchoron (1800 vertices, rectangular trapezohedron vertex figure) - rhombitriacontaswirlic chilliaoctacosichoron (1800 rhombic antiprism cells)

20. Octacontafold icosidodecaswirlchoron (2400 vertices) - rhombitriacontaswirlic dischilliatetracosichoron (2400 cells)

25. Hectofold icosidodecaswirlchoron (3000 vertices) - rhombitriacontaswirlic trischilliachoron (3000 cells)

30. Hecatonicosafold icosidodecaswirlchoron (3600 vertices) - rhombitriacontaswirlic trischilliahexacosichoron (3600 cells)

Triangular dihedron-based
1. Triangular duotegum (6 vertices, tetragonal disphenoid vertex figure) - triangular duoprism (6 triangular prisms)

2. 9-2 step prism (9 vertices, ridge-triakis bi-apiculated tetrahedron vertex figure) - 9-2 gyrochoron (9 ridge-truncated edge-truncated tetrahedra)

3. Hexagonal duotegum (12 vertices, tetragonal disphenoid vertex figure) - hexagonal duoprism (12 triangular prisms)

4. 15-4 step prism (15 vertices, paratetraaugmented digonal scalenohedron vertex figure) - 15-4 gyrochoron (15 paratetratruncated rhombic prisms)

5. 18-5 step prism (18 vertices, metabitriakis snub disphenoid vertex figure) - 18-5 gyrochoron (18 metabitruncated elongated gyrobifastigia)

6. 21-8 step prism (21 vertices) - 21-8 gyrochoron (21 cells)

7. 24-5 step prism (24 vertices) - 24-5 gyrochoron (24 cells)

8. 27-8 step prism (27 vertices) - 27-8 gyrochoron (27 cells)

9. 30-11 step prism (30 vertices) - 30-11 gyrochoron (30 cells)

10. 33-10 step prism (33 vertices) - 33-10 gyrochoron (33 cells)

Square dihedron-based
1. Hexadecachoron (8 vertices, octahedron vertex figure) - tesseract (8 cubes)

2. Hexagonal duotegum (12 vertices, tetragonal disphenoid vertex figure) - hexagonal duoprism (12 triangular prisms)

3. 16-3 step prism (16 vertices) - 16-3 gyrochoron (16 cells)

4. Decagonal duotegum (20 vertices, decagonal bipyramid vertex figure) - decagonal duoprism (20 decagonal prisms)

5. 24-5 step prism (24 vertices) - 24-5 gyrochoron (24 cells)

6. Tetradecagonal duotegum (28 vertices, tetradecagonal bipyramid vertex figure) - tetradecagonal duoprism (28 tetradecagonal prisms)

7. 32-7 step prism (32 vertices) - 32-7 gyrochoron (32 cells)

8. Octadecagonal duotegum (36 vertices, octadecagonal bipyramid vertex figure) - octadecagonal duoprism (36 octadecagonal prisms)

9. 40-9 step prism (40 vertices) - 40-9 gyrochoron (40 cells)

10. Icosidigonal duotegum (44 vertices, icosidigonal bipyramid vertex figure) - icosidigonal duoprism (44 icosidigonal prisms)

Pentagonal dihedron-based
1. Pentagonal duotegum (10 vertices, pentagonal bipyramid vertex figure) - pentagonal duoprism (10 pentagonal prisms)

2. 15-2 step prism (15 vertices, ridge-quadritriakis bi-apiculated tetrahedron vertex figure) - 15-2 gyrochoron (12 ridge-quadritruncated edge-truncated tetrahedra)

3. 20-3 step prism (20 vertices) - 20-3 gyrochoron (20 cells)

4. 25-4 step prism (25 vertices) - 25-4 gyrochoron (20 cells)

5. 30-7 step prism (30 vertices) - 30-7 gyrochoron (30 cells)

6. 35-6 step prism (35 vertices) - 35-6 gyrochoron (35 cells)

7. 40-7 step prism (40 vertices) - 40-7 gyrochoron (40 cells)

8. 45-8 step prism (45 vertices) - 45-8 gyrochoron (45 cells)

9. 50-9 step prism (50 vertices) - 50-9 gyrochoron (50 cells)

10. 55-12 step prism (55 vertices) - 55-12 gyrochoron (55 cells)

Hexagonal dihedron-based
1. Hexagonal duotegum (12 vertices, hexagonal bipyramid vertex figure) - hexagonal duoprism (12 hexagonal prisms)

2. 18-5 step prism (18 vertices, metabitriakis snub disphenoid vertex figure) - 18-5 gyrochoron (18 metabitruncated elongated gyrobifastigia)

3. 24-5 step prism (24 vertices) - 24-5 gyrochoron (24 cells)

4. 30-11 step prism (30 vertices) - 30-11 gyrochoron (30 cells)

5. 36-5 step prism (36 vertices) - 36-5 gyrochoron (36 cells)

6. 42-13 step prism (42 vertices) - 42-13 gyrochoron (42 cells)

7. 48-7 step prism (48 vertices) - 48-7 gyrochoron (48 cells)

8. 54-17 step prism (54 vertices) - 54-17 gyrochoron (54 cells)

9. 60-11 step prism (60 vertices) - 60-11 gyrochoron (60 cells)

10. 66-23 step prism (66 vertices) - 66-23 gyrochoron (66 cells)

Digonal antiprism-based
1. Hexadecachoron (8 vertices, octahedron vertex figure) - tesseract (16 cubes)

2. Digonal double antiprismoid (16 vertices, hexakis digonal-hexagonal gyrowedge vertex figure) - digonal double trapezohedroid (16 order-6 truncated digonal-hexagonal gyronotches)

3. 24-7 step prism (24 vertices, paratetraaugmented hexagonal bipyramid vertex figure) - 24-7 gyrochoron (24 paratetratruncated hexagonal prisms)

4. Digonal double tetraswirlprism (32 vertices) - digonal double tetraswirltegum (32 cells)

Triangular antiprism-based
1. Triangular duoantiprism (18 vertices, gyrobifastigium vertex figure) - triangular duoantitegum (18 elongated tetragonal disphenoids)

2. Triangular double antiprismoid (36 vertices, sphenocorona vertex figure) - triangular double trapezohedroid (36 order-5 truncated bi-apiculated tetrahedra)

3. Triangular double triswirlprism (54 vertices) - triangular double triswirltegum (54 cells)

4. Triangular double tetraswirlprism (72 vertices) - triangular double tetraswirltegum (72 cells)

Square antiprism-based
1. Square duoantiprism (32 vertices, gyrobifastigium vertex figure) - square duoantitegum (32 elongated tetragonal disphenoids)

2. Square double antiprismoid (64 vertices, sphenocorona vertex figure) - square double trapezohedroid (64 order-5 truncated bi-apiculated tetrahedra)

3. Square double triswirlprism (96 vertices) - square double triswirltegum (96 cells)

4. Square double tetraswirlprism (128 vertices) - square double tetraswirltegum (128 cells)

Pentagonal antiprism-based
1. Pentagonal duoantiprism (50 vertices, gyrobifastigium vertex figure) - pentagonal duoantitegum (50 elongated tetragonal disphenoids)

2. Grand antiprism (100 vertices, sphenocorona vertex figure) - pentagonal double trapezohedroid (100 order-5 truncated bi-apiculated tetrahedra)

3. Pentagonal double triswirlprism (150 vertices) - pentagonal double triswirltegum (150 cells)

4. Pentagonal double tetraswirlprism (200 vertices) - pentagonal double tetraswirltegum (200 cells)

Hexagonal antiprism-based
1. Hexagonal duoantiprism (72 vertices, gyrobifastigium vertex figure) - hexagonal duoantitegum (72 elongated tetragonal disphenoids)

2. Hexagonal double antiprismoid (144 vertices, sphenocorona vertex figure) - hexagonal double trapezohedroid (144 order-5 truncated bi-apiculated tetrahedra)

3. Hexagonal double triswirlprism (216 vertices) - hexagonal double triswirltegum (216 cells)

4. Hexagonal double tetraswirlprism (288 vertices) - hexagonal double tetraswirltegum (288 cells)