The
There are still a few restrictions, however:
The Desmos graph I used to test the formulae an be found here. All the info about these were generated using a Python program. The quadriverticed circumradii were calculating with the circumradius of x3/2x(x)o(y)*a, with (x) and (y) being the polygons in a 3.3.x.y configuration.
Note that the vertex count is simply extrapolated from the usual method of calculating by the fact that summing the missing vertex angles of any convex polyhedron results in 720°. Their actual vertex count is infinite as they are dense.
| Vert. Conf. | Name | Vertices | Circumradius | Dihedral angles |
|---|---|---|---|---|
| 3.3.4 | Square pyramidoid | 4.8 (4+4/5) | 0.70710678 | 3–3: 109.471°, 3–4: 54.736°, 4–3: 54.736° |
| 3.3.5 | Pentagonal pyramidoid | 5.455 (5+5/11) | 0.95105652 | 3–3: 138.19°, 3–5: 37.377°, 5–3: 37.377° |
| 3.4.5 | Pentagonal tetrapyramidoid | 7.059 (7+1/17) | 0.8660254 | 3–4: 110.905°, 4–5: 58.283°, 5–3: 79.188° |
| 3.4.6 | Hexagonal tetrapyramidoid | 8 | 1 | 3–4: 125.264°, 4–6: 54.736°, 6–3: 70.529° |
| 3.4.7 | Heptagonal tetrapyramidoid | 8.842 (8+16/19) | 1.17195981 | 3–4: 136.05°, 4–7: 50.244°, 7–3: 62.586° |
| 3.4.8 | Octagonal tetrapyramidoid | 9.6 (9+3/5) | 1.39896633 | 3–4: 144.736°, 4–8: 45°, 8–3: 54.736° |
| 3.4.9 | Enneagonal tetrapyramidoid | 10.286 (10+2/7) | 1.71922572 | 3–4: 152.196°, 4–9: 38.935°, 9–3: 46.523° |
| 3.4.10 | Decagonal tetrapyramidoid | 10.909 (10+10/11) | 2.23295051 | 3–4: 159.095°, 4–10: 31.717°, 10–3: 37.377° |
| 3.4.11 | Hendecagonal tetrapyramidoid | 11.478 (11+11/23) | 3.33677158 | 3–4: 166.263°, 4–11: 22.358°, 11–3: 26.055° |
| 3.5.5 | Pentagonal pentapyramidoid | 8.571 (8+4/7) | 0.95105652 | 3–5: 100.812°, 5–5: 63.435°, 5–3: 100.812° |
| 3.5.6 | Hexagonal pentapyramidoid | 10 | 1.06212772 | 3–5: 114.801°, 5–6: 65.199°, 6–3: 94.513° |
| 3.5.7 | Heptagonal pentapyramidoid | 11.351 (11+13/37) | 1.18698035 | 3–5: 124.708°, 5–7: 65.586°, 7–3: 89.769° |
| 3.5.8 | Octagonal pentapyramidoid | 12.632 (12+12/19) | 1.32199705 | 3–5: 132.138°, 5–8: 65.255°, 8–3: 85.829° |
| 3.5.9 | Enneagonal pentapyramidoid | 13.846 (13+11/13) | 1.4658125 | 3–5: 137.943°, 5–9: 64.49°, 9–3: 82.36° |
| 3.5.10 | Decagonal pentapyramidoid | 15 | 1.61803399 | 3–5: 142.623°, 5–10: 63.435°, 10–3: 79.188° |
| 3.5.11 | Hendecagonal pentapyramidoid | 16.098 (16+4/41) | 1.77883396 | 3–5: 146.49°, 5–11: 62.171°, 11–3: 76.209° |
| 3.5.12 | Dodecagonal pentapyramidoid | 17.143 (17+1/7) | 1.94879366 | 3–5: 149.754°, 5–12: 60.746°, 12–3: 73.36° |
| 3.5.13 | Tridecagonal pentapyramidoid | 18.14 (18+6/43) | 2.1288491 | 3–5: 152.556°, 5–13: 59.19°, 13–3: 70.596° |
| 3.5.14 | Tetradecagonal pentapyramidoid | 19.091 (19+1/11) | 2.32029289 | 3–5: 154.998°, 5–14: 57.521°, 14–3: 67.884° |
| 3.5.15 | Pentadecagonal pentapyramidoid | 20 | 2.52481765 | 3–5: 157.156°, 5–15: 55.752°, 15–3: 65.199° |
| 3.5.16 | Hexadecagonal pentapyramidoid | 20.87 (20+20/23) | 2.74460044 | 3–5: 159.085°, 5–16: 53.887°, 16–3: 62.521° |
| 3.5.17 | Heptadecagonal pentapyramidoid | 21.702 (21+33/47) | 2.98243745 | 3–5: 160.829°, 5–17: 51.93°, 17–3: 59.831° |
| 3.5.18 | Octadecagonal pentapyramidoid | 22.5 (22+1/2) | 3.24194919 | 3–5: 162.423°, 5–18: 49.877°, 18–3: 57.113° |
| 3.5.19 | Enneadecagonal pentapyramidoid | 23.265 (23+13/49) | 3.52789245 | 3–5: 163.893°, 5–19: 47.726°, 19–3: 54.35° |
| 3.5.20 | Icosagonal pentapyramidoid | 24 | 3.84664395 | 3–5: 165.264°, 5–20: 45.468°, 20–3: 51.523° |
| 3.5.21 | Icosihenagonal pentapyramidoid | 24.706 (24+12/17) | 4.20697418 | 3–5: 166.554°, 5–21: 43.092°, 21–3: 48.612° |
| 3.5.22 | Icosidigonal pentapyramidoid | 25.385 (25+5/13) | 4.62133821 | 3–5: 167.782°, 5–22: 40.581°, 22–3: 45.593° |
| 3.5.23 | Icositrigonal pentapyramidoid | 26.038 (26+2/53) | 5.10814607 | 3–5: 168.964°, 5–23: 37.911°, 23–3: 42.436° |
| 3.5.24 | Icositetragonal pentapyramidoid | 26.667 (26+2/3) | 5.69603162 | 3–5: 170.117°, 5–24: 35.05°, 24–3: 39.1° |
| 3.5.25 | Icosipentagonal pentapyramidoid | 27.273 (27+3/11) | 6.43260236 | 3–5: 171.26°, 5–25: 31.948°, 25–3: 35.529° |
| 3.5.26 | Icosihexagonal pentapyramidoid | 27.857 (27+6/7) | 7.40456989 | 3–5: 172.416°, 5–26: 28.531°, 26–3: 31.637° |
| 3.5.27 | Icosiheptagonal pentapyramidoid | 28.421 (28+8/19) | 8.79231879 | 3–5: 173.619°, 5–27: 24.668°, 27–3: 27.28° |
| 3.5.28 | Icosioctagonal pentapyramidoid | 28.966 (28+28/29) | 11.06106306 | 3–5: 174.932°, 5–28: 20.108°, 28–3: 22.181° |
| 3.5.29 | Icosienneagonal pentapyramidoid | 29.492 (29+29/59) | 16.05118514 | 3–5: 176.511°, 5–29: 14.194°, 29–3: 15.621° |
| 3.6.x, x≥7 | Hexapyramidoids (infinite family) | 2x | ||
| 3.7.7 | Heptagonal heptatruncatoid | 16.8 (16+4/5) | 1.44012994 | 3–7: 117.414°, 7–7: 79.513°, 7–3: 117.414° |
| 3.7.8 | Octagonal heptatruncatoid | 19.765 (19+13/17) | 1.59475501 | 3–7: 125.727°, 7–8: 83.86°, 8–3: 116.155° |
| 3.7.9 | Enneagonal heptatruncatoid | 22.909 (22+10/11) | 1.75890693 | 3–7: 132.141°, 7–9: 87.448°, 9–3: 115.593° |
| 3.7.10 | Decagonal heptatruncatoid | 26.25 (26+1/4) | 1.93055208 | 3–7: 137.259°, 7–10: 90.55°, 10–3: 115.479° |
| 3.7.11 | Hendecagonal heptatruncatoid | 29.806 (29+25/31) | 2.10875285 | 3–7: 141.448°, 7–11: 93.325°, 11–3: 115.676° |
| 3.7.12 | Dodecagonal heptatruncatoid | 33.6 (33+3/5) | 2.29312836 | 3–7: 144.948°, 7–12: 95.867°, 12–3: 116.097° |
| 3.7.13 | Tridecagonal heptatruncatoid | 37.655 (37+19/29) | 2.48362675 | 3–7: 147.922°, 7–13: 98.24°, 13–3: 116.689° |
| 3.7.14 | Tetradecagonal heptatruncatoid | 42 | 2.68041722 | 3–7: 150.486°, 7–14: 100.487°, 14–3: 117.414° |
| 3.7.15 | Pentadecagonal heptatruncatoid | 46.667 (46+2/3) | 2.88383632 | 3–7: 152.724°, 7–15: 102.64°, 15–3: 118.249° |
| 3.7.16 | Hexadecagonal heptatruncatoid | 51.692 (51+9/13) | 3.09436211 | 3–7: 154.699°, 7–16: 104.721°, 16–3: 119.174° |
| 3.7.17 | Heptadecagonal heptatruncatoid | 57.12 (57+3/25) | 3.31260463 | 3–7: 156.457°, 7–17: 106.748°, 17–3: 120.176° |
| 3.7.18 | Octadecagonal heptatruncatoid | 63 | 3.53930722 | 3–7: 158.037°, 7–18: 108.735°, 18–3: 121.246° |
| 3.7.19 | Enneadecagonal heptatruncatoid | 69.391 (69+9/23) | 3.77535632 | 3–7: 159.467°, 7–19: 110.694°, 19–3: 122.378° |
| 3.7.20 | Icosagonal heptatruncatoid | 76.364 (76+4/11) | 4.02179901 | 3–7: 160.771°, 7–20: 112.633°, 20–3: 123.565° |
| 3.7.21 | Icosihenagonal heptatruncatoid | 84 | 4.27986869 | 3–7: 161.967°, 7–21: 114.561°, 21–3: 124.805° |
| 3.7.22 | Icosidigonal heptatruncatoid | 92.4 (92+2/5) | 4.55102011 | 3–7: 163.072°, 7–22: 116.486°, 22–3: 126.096° |
| 3.7.23 | Icositrigonal heptatruncatoid | 101.684 (101+13/19) | 4.8369762 | 3–7: 164.097°, 7–23: 118.413°, 23–3: 127.436° |
| 3.7.24 | Icositetragonal heptatruncatoid | 112 | 5.13979018 | 3–7: 165.054°, 7–24: 120.35°, 24–3: 128.825° |
| 3.7.25 | Icosipentagonal heptatruncatoid | 123.529 (123+9/17) | 5.46192837 | 3–7: 165.953°, 7–25: 122.302°, 25–3: 130.264° |
| 3.7.26 | Icosihexagonal heptatruncatoid | 136.5 (136+1/2) | 5.80638149 | 3–7: 166.8°, 7–26: 124.276°, 26–3: 131.755° |
| 3.7.27 | Icosiheptagonal heptatruncatoid | 151.2 (151+1/5) | 6.17681657 | 3–7: 167.604°, 7–27: 126.277°, 27–3: 133.299° |
| 3.7.28 | Icosioctagonal heptatruncatoid | 168 | 6.5777875 | 3–7: 168.369°, 7–28: 128.314°, 28–3: 134.899° |
| 3.7.29 | Icosienneagonal heptatruncatoid | 187.385 (187+5/13) | 7.01503301 | 3–7: 169.102°, 7–29: 130.392°, 29–3: 136.561° |
| 3.7.30 | Triacontagonal heptatruncatoid | 210 | 7.495908 | 3–7: 169.808°, 7–30: 132.522°, 30–3: 138.29° |
| 3.7.31 | Triacontahenagonal heptatruncatoid | 236.727 (236+8/11) | 8.03002533 | 3–7: 170.492°, 7–31: 134.713°, 31–3: 140.092° |
| 3.7.32 | Triacontadigonal heptatruncatoid | 268.8 (268+4/5) | 8.6302409 | 3–7: 171.159°, 7–32: 136.977°, 32–3: 141.978° |
| 3.7.33 | Triacontatrigonal heptatruncatoid | 308 | 9.31422326 | 3–7: 171.812°, 7–33: 139.328°, 33–3: 143.959° |
| 3.7.34 | Triacontatetragonal heptatruncatoid | 357 | 10.10706801 | 3–7: 172.458°, 7–34: 141.785°, 34–3: 146.05° |
| 3.7.35 | Triacontapentagonal heptatruncatoid | 420 | 11.04589451 | 3–7: 173.102°, 7–35: 144.372°, 35–3: 148.272° |
| 3.7.36 | Triacontahexagonal heptatruncatoid | 504 | 12.18849149 | 3–7: 173.751°, 7–36: 147.122°, 36–3: 150.654° |
| 3.7.37 | Triacontaheptagonal heptatruncatoid | 621.6 (621+3/5) | 13.63104704 | 3–7: 174.414°, 7–37: 150.081°, 37–3: 153.238° |
| 3.7.38 | Triacontaoctagonal heptatruncatoid | 798 | 15.54896593 | 3–7: 175.105°, 7–38: 153.322°, 38–3: 156.089° |
| 3.7.39 | Triacontaenneagonal heptatruncatoid | 1092 | 18.30759585 | 3–7: 175.844°, 7–39: 156.966°, 39–3: 159.315° |
| 3.7.40 | Tetracontagonal heptatruncatoid | 1680 | 22.85040712 | 3–7: 176.671°, 7–40: 161.248°, 40–3: 163.129° |
| 3.7.41 | Tetracontahenagonal heptatruncatoid | 3444 | 32.91508097 | 3–7: 177.69°, 7–41: 166.779°, 41–3: 168.084° |
| 3.8.9 | Enneagonal octatruncatoid | 28.8 (28+4/5) | 1.98224354 | 3–8: 132.345°, 8–9: 95.261°, 9–3: 125.604° |
| 3.8.10 | Decagonal octatruncatoid | 34.286 (34+2/7) | 2.20403635 | 3–8: 138.053°, 8–10: 99.984°, 10–3: 126.474° |
| 3.8.11 | Hendecagonal octatruncatoid | 40.615 (40+8/13) | 2.44531855 | 3–8: 142.789°, 8–11: 104.367°, 11–3: 127.724° |
| 3.8.12 | Dodecagonal octatruncatoid | 48 | 2.70867773 | 3–8: 146.81°, 8–12: 108.532°, 12–3: 129.271° |
| 3.8.13 | Tridecagonal octatruncatoid | 56.727 (56+8/11) | 2.99813927 | 3–8: 150.296°, 8–13: 112.568°, 13–3: 131.064° |
| 3.8.14 | Tetradecagonal octatruncatoid | 67.2 (67+1/5) | 3.31947321 | 3–8: 153.371°, 8–14: 116.539°, 14–3: 133.075° |
| 3.8.15 | Pentadecagonal octatruncatoid | 80 | 3.68085205 | 3–8: 156.13°, 8–15: 120.501°, 15–3: 135.291° |
| 3.8.16 | Hexadecagonal octatruncatoid | 96 | 4.09403581 | 3–8: 158.644°, 8–16: 124.503°, 16–3: 137.711° |
| 3.8.17 | Heptadecagonal octatruncatoid | 116.571 (116+4/7) | 4.57650698 | 3–8: 160.974°, 8–17: 128.599°, 17–3: 140.348° |
| 3.8.18 | Octadecagonal octatruncatoid | 144 | 5.15551555 | 3–8: 163.169°, 8–18: 132.846°, 18–3: 143.228° |
| 3.8.19 | Enneadecagonal octatruncatoid | 182.4 (182+2/5) | 5.87638774 | 3–8: 165.276°, 8–19: 137.322°, 19–3: 146.394° |
| 3.8.20 | Icosagonal octatruncatoid | 240 | 6.82164699 | 3–8: 167.348°, 8–20: 142.133°, 20–3: 149.921° |
| 3.8.21 | Icosihengonal octatruncatoid | 336 | 8.16282798 | 3–8: 169.449°, 8–21: 147.454°, 21–3: 153.943° |
| 3.8.22 | Icosidigonal octatruncatoid | 528 | 10.34187538 | 3–8: 171.688°, 8–22: 153.616°, 22–3: 158.725° |
| 3.8.23 | Icositrigonal octatruncatoid | 1104 | 15.10507357 | 3–8: 174.318°, 8–23: 161.47°, 23–3: 164.961° |
| 3.9.9 | Enneagonal enneatruncatoid | 36 | 2.24242099 | 3–9: 133.477°, 9–9: 102.13°, 9–3: 133.477° |
| 3.9.10 | Decagonal enneatruncatoid | 45 | 2.54360186 | 3–9: 139.93°, 9–10: 108.477°, 10–3: 135.254° |
| 3.9.11 | Hendecagonal enneatruncatoid | 56.571 (56+4/7) | 2.89602966 | 3–9: 145.403°, 9–11: 114.559°, 11–3: 137.54° |
| 3.9.12 | Dodecagonal enneatruncatoid | 72 | 3.31766778 | 3–9: 150.188°, 9–12: 120.561°, 12–3: 140.273° |
| 3.9.13 | Tridecagonal enneatruncatoid | 93.6 (93+3/5) | 3.83952518 | 3–9: 154.498°, 9–13: 126.647°, 13–3: 143.451° |
| 3.9.14 | Tetragonal enneatruncatoid | 126 | 4.51874447 | 3–9: 158.503°, 9–14: 132.993°, 14–3: 147.119° |
| 3.9.15 | Pentagonal enneatruncatoid | 180 | 5.47448714 | 3–9: 162.369°, 9–15: 139.843°, 15–3: 151.402° |
| 3.9.16 | Hexagonal enneatruncatoid | 288 | 7.01374594 | 3–9: 166.311°, 9–16: 147.618°, 16–3: 156.578° |
| 3.9.17 | Heptagonal enneatruncatoid | 612 | 10.34792914 | 3–9: 170.762°, 9–17: 157.364°, 17–3: 163.402° |
| 3.10.11 | Hendecagonal decatruncatoid | 82.5 (82+1/2) | 3.52549375 | 3–10: 149.091°, 10–11: 124.63°, 11–3: 146.05° |
| 3.10.12 | Dodecagonal decatruncatoid | 120 | 4.30673898 | 3–10: 155.046°, 10–12: 133.052°, 12–3: 150.267° |
| 3.10.13 | Tridecagonal decatruncatoid | 195 | 5.56002905 | 3–10: 160.877°, 10–13: 142.376°, 13–3: 155.522° |
| 3.10.14 | Tetradecagonal decatruncatoid | 420 | 8.26045496 | 3–10: 167.237°, 10–14: 153.836°, 14–3: 162.586° |
| 3.11.11 | Hendecagonal hendecatruncatoid | 132 | 4.50447394 | 3–11: 153.945°, 11–11: 135.285°, 11–3: 153.945° |
| 3.11.12 | Dodecagonal hendecatruncatoid | 264 | 6.43955436 | 3–11: 162.042°, 11–12: 147.722°, 12–3: 160.526° |
| 3.11.13 | Tridecagonal hendecatruncatoid | 1716 | 16.59820836 | 3–11: 173.112°, 11–13: 167.086°, 13–3: 171.98° |
| 4.5.5 | Pentagonal pentagrombatoid | 13.333 (13+1/3) | 1.14412281 | 4–5: 108.961°, 5–5: 96.06°, 5–4: 108.961° |
| 4.5.6 | Hexagonal pentagrombatoid | 17.143 (17+1/7) | 1.32287566 | 4–5: 121.717°, 5–6: 100.812°, 6–4: 110.905° |
| 4.5.7 | Heptagonal pentagrombatoid | 21.538 (21+7/13) | 1.51993462 | 4–5: 130.963°, 5–7: 105.018°, 7–4: 113.281° |
| 4.5.8 | Octagonal pentagrombatoid | 26.667 (26+2/3) | 1.73555662 | 4–5: 138.03°, 5–8: 108.961°, 8–4: 115.914° |
| 4.5.9 | Enneagonal pentagrombatoid | 32.727 (32+8/11) | 1.9719251 | 4–5: 143.655°, 5–9: 112.782°, 9–4: 118.734° |
| 4.5.10 | Decagonal pentagrombatoid | 40 | 2.23295051 | 4–5: 148.283°, 5–10: 116.565°, 10–4: 121.717° |
| 4.5.11 | Hendecagonal pentagrombatoid | 48.889 (48+8/9) | 2.52458442 | 4–5: 152.196°, 5–11: 120.37°, 11–4: 124.86° |
| 4.5.12 | Dodecagonal pentagrombatoid | 60 | 2.85562786 | 4–5: 155.587°, 5–12: 124.248°, 12–4: 128.173° |
| 4.5.13 | Tridecagonal pentagrombatoid | 74.286 (74+2/7) | 3.23930293 | 4–5: 158.595°, 5–13: 128.249°, 13–4: 131.678° |
| 4.5.14 | Tetradecagonal pentagrombatoid | 93.333 (93+1/3) | 3.69629437 | 4–5: 161.322°, 5–14: 132.431°, 14–4: 135.415° |
| 4.5.15 | Pentadecagonal pentagrombatoid | 120 | 4.26103434 | 4–5: 163.854°, 5–15: 136.868°, 15–4: 139.442° |
| 4.5.16 | Hexadecagonal pentagrombatoid | 160 | 4.99618463 | 4–5: 166.27°, 5–16: 141.668°, 16–4: 143.852° |
| 4.5.17 | Heptadecagonal pentagrombatoid | 226.667 (226+2/3) | 6.0318762 | 4–5: 168.655°, 5–17: 147.005°, 17–4: 148.807° |
| 4.5.18 | Octadecagonal pentagrombatoid | 360 | 7.70300825 | 4–5: 171.134°, 5–18: 153.216°, 18–4: 154.623° |
| 4.5.19 | Enneadecagonal pentagrombatoid | 760 | 11.33123094 | 4–5: 173.983°, 5–19: 161.166°, 19–4: 162.12° |
| 4.6.7 | Heptagonal grombatoid | 33.6 (33+3/5) | 1.90275311 | 4–6: 136.05°, 6–7: 117.414°, 7–4: 129.756° |
| 4.6.9 | Enneagonal grombatoid | 72 | 2.89261321 | 4–6: 152.196°, 6–9: 133.477°, 9–4: 141.065° |
| 4.6.11 | Hendecagonal grombatoid | 264 | 5.73603815 | 4–6: 166.263°, 6–11: 153.945°, 11–4: 157.642° |
| 4.7.7 | Heptagonal heptagrombatoid | 56 | 2.48443296 | 4–7: 142.89°, 7–7: 129.492°, 7–4: 142.89° |
| 4.7.8 | Octagonal heptagrombatoid | 112 | 3.56438987 | 4–7: 154.746°, 7–8: 142.89°, 8–4: 151.854° |
| 4.7.9 | Enneagonal heptagrombatoid | 504 | 7.67565724 | 4–7: 168.466°, 7–9: 161.877°, 9–4: 165.925° |
| 5.5.6 | Hexagonal cosmoid | 30 | 1.73854608 | 5–5: 131.175°, 5–6: 124.248°, 6–5: 124.248° |
| 5.5.7 | Heptagonal cosmoid | 46.667 (46+2/3) | 2.20635222 | 5–5: 142.645°, 5–7: 132.431°, 7–5: 132.431° |
| 5.5.8 | Octagonal cosmoid | 80 | 2.942284 | 5–5: 152.54°, 5–8: 141.668°, 8–5: 141.668° |
| 5.5.9 | Enneagonal cosmoid | 180 | 4.49304373 | 5–5: 162.268°, 5–9: 153.216°, 9–5: 153.216° |
| 5.6.7 | Heptagonal hexacosmoid | 210 | 4.69618173 | 5–6: 160.837°, 6–7: 156.465°, 7–5: 158.678° |
| Vert. Conf. | Name | Vertices | Circumradius | Dihedral angles |
|---|---|---|---|---|
| 3.3.4.4 | Square tetrarectoid Metacuboctahedron |
12 | 1 | |
| 3.3.4.5 | Pentagonal tetrametarectoid | 17.143 (17+1/7) | 1.21514193 | |
| 3.3.4.6 | Hexagonal tetrametarectoid | 24 | 1.47260268 | |
| 3.3.4.7 | Heptagonal tetrametarectoid | 33.6 (33+3/5) | 1.78710318 | |
| 3.3.4.8 | Octagonal tetrametarectoid | 48 | 2.18885876 | |
| 3.3.4.9 | Enneagonal tetrametarectoid | 72 | 2.74250029 | |
| 3.3.4.10 | Decagonal tetrametarectoid | 120 | 3.6151889 | |
| 3.3.4.11 | Hendecagonal tetrametarectoid | 264 | 5.46508259 | |
| 3.4.3.5 | Pentagonal tetrapararectoid | 17.143 (17+1/7) | 1.21514193 | |
| 3.4.3.6 | Hexagonal tetrapararectoid | 24 | 1.47260268 | |
| 3.4.3.7 | Heptagonal tetrapararectoid | 33.6 (33+3/5) | 1.78710318 | |
| 3.4.3.8 | Octagonal tetrapararectoid | 48 | 2.18885876 | |
| 3.4.3.9 | Enneagonal tetrapararectoid | 72 | 2.74250029 | |
| 3.4.3.10 | Decagonal tetrapararectoid | 120 | 3.6151889 | |
| 3.4.3.11 | Hendecagonal tetrapararectoid | 264 | 5.46508259 | |
| 3.3.5.5 | Pentagonal pentametarectoid Metaicosidodecahedron |
30 | 1.61803399 | |
| 3.3.5.6 | Hexagonal pentametarectoid | 60 | 2.32442133 | |
| 3.3.5.7 | Heptagonal pentametarectoid | 210 | 4.42745625 | |
| 3.5.3.6 | Hexagonal pentapararectoid | 60 | 2.32442133 | |
| 3.5.3.7 | Heptagonal pentapararectoid | 210 | 4.42745625 | |
| 3.4.4.5 | Pentagonal bitetrarectoid Metarhombicosidodecahedron |
60 | 2.23295051 |