Seznam sestavov enotnih poliedrov vsebuje sestave poliedrov, ki jih sestavljajo enaki (po možnosti enanciomorfni) enotni poliedri, in sicer v taki razvrstitvi, da dobimo prav tako enotna telesa. Somerna skupina sestave deluje prehodno na oglišča sestavljenega telesa.
Enotne poliedre je prvi oštevilčil John Skilling (1921–1998) leta 1976 in pokazal, da je številčenje popolno. Spodnji seznam vsebuje vse njegove sestave in njegovo številčenje.
sestav | Bowerjeva okrajšava |
slika | število poliedrov |
Vrsta poliedra | sStranske ploskve | robovi | oglišča | spombe | simetrijska grupa | podgrupa omejena na en sestavni del |
---|---|---|---|---|---|---|---|---|---|---|
UC01 | sis | ![]() |
6 | tetraedri | 24{3} | 36 | 24 | vrtilna prostost | Td | S4 |
UC02 | dis | ![]() |
12 | tetraedri | 48{3} | 72 | 48 | vrtilna svoboda | Oh | S4 |
UC03 | snu | ![]() |
6 | tetraedri | 24{3} | 36 | 24 | Oh | D2d | |
UC04 | so | ![]() |
2 | tetraedri | 8{3} | 12 | 8 | pravilni | Oh | Td |
UC05 | ki | ![]() |
5 | tetraedri | 20{3} | 30 | 20 | pravilni | I | T |
UC06 | e | ![]() |
10 | tetraedri | 40{3} | 60 | 20 | pravilni
2 sestavna dela poliedra vpadata v vsakem oglišču |
Ih | T |
UC07 | risdoh | ![]() |
6 | kocke | (12+24){4} | 72 | 48 | vrtilna svoboda | Oh | C4h |
UC08 | rah | ![]() |
3 | kocke | (6+12){4} | 36 | 24 | Oh | D4h | |
UC09 | rhom | ![]() |
5 | kocke | 30{4} | 60 | 20 | pravilni
2 sestavna dela poliedra vpadata v vsako oglišče |
Ih | Th |
UC10 | dissit | ![]() |
4 | oktaedri | (8+24){3} | 48 | 24 | vrtilna svoboda | Th | S6 |
UC11 | doso | ![]() |
8 | oktaedri | (16+48){3} | 96 | 48 | vrtilna svoboda | Oh | S6 |
UC12 | sno | ![]() |
4 | oktaedri | (8+24){3} | 48 | 24 | Oh | D3d | |
UC13 | addasi | ![]() |
20 | oktaedri | (40+120){3} | 240 | 120 | vrtilna svoboda | Ih | S6 |
UC14 | dasi | ![]() |
20 | oktaedri | (40+120){3} | 240 | 60 | 2 sestavna dela poliedra vpadata v vsako oglišče | Ih | S6 |
UC15 | gissi | ![]() |
10 | oktaedri | (20+60){3} | 120 | 60 | Ih | D3d | |
UC16 | si | ![]() |
10 | oktaedri | (20+60){3} | 120 | 60 | Ih | D3d | |
UC17 | se | ![]() |
5 | oktaedri | 40{3} | 60 | 30 | pravilni | Ih | Th |
UC18 | hirki | ![]() |
5 | tetrahemiheksaedri | 20{3}
15{4} |
60 | 30 | I | T | |
UC19 | sapisseri | ![]() |
20 | tetrahemiheksaedri | (20+60){3}
60{4} |
240 | 60 | 2 sestavna dela poliedra vpadata v vsako oglišče | I | C3 |
UC20 | - | ![]() |
2n
(n>0) |
p/q-strane prizme | 4n{p/q}
2np{4} |
6np | 4np | vrtilna svoboda
gcd(p,q)=1, p/q>2 |
Dnph | Cph |
UC21 | - | ![]() |
n
(n>1) |
p/q-strane prizme | 2n{p/q}
np{4} |
3np | 2np | gcd(p,q)=1, p/q>2 | Dnph | Dph |
UC22 | - | ![]() |
2n
(n>0) |
p/q-strane antiprizme (tetraedri če je p/q=2)
(q neparen) |
4n{p/q} (sicer p/q=2)
4np{3} |
8np | 4np | vrtilna svoboda
gcd(p,q)=1, p/q>3/2 |
Dnpd (če je n neparen)
Dnph (če je n paren) |
S2p |
UC23 | - | ![]() |
n
(n>1) |
p/q-strane antiprizme (tetraedri če je p/q=2)
(q neparen) |
2n{p/q} (sicer p/q=2)
2np{3} |
4np | 2np | gcd(p,q)=1, p/q>3/2 | Dnpd (če je n neparen)
Dnph (če je n paren) |
Dpd |
UC24 | - | ![]() |
2n
(n>0) |
p/q-strane antiprizme
(q paren) |
4n{p/q}
4np{3} |
8np | 4np | vrtilna svoboda
gcd(p,q)=1, p/q>3/2 |
Dnph | Cph |
UC25 | - | ![]() |
n
(n>1) |
p/q-strane antiprizme
(q paren) |
2n{p/q}
2np{3} |
4np | 2np | gcd(p,q)=1, p/q>3/2 | Dnph | Dph |
UC26 | gadsid | ![]() |
12 | petstrane antiprizme | 120{3}
24{5} |
240 | 120 | vrtilna svoboda | Ih | S10 |
UC27 | gassid | ![]() |
6 | petstrane antiprizme | 60{3}
12{5} |
120 | 60 | Ih | D5d | |
UC28 | gidasid | ![]() |
12 | pentagramske križne antiprizme | 120{3}
24{5/2} |
240 | 120 | vrtilna svoboda | Ih | S10 |
UC29 | gissed | ![]() |
6 | pentagramske križne antiprizme | 60{3}
12{5/2} |
120 | 60 | Ih | D5d | |
UC30 | ro | ![]() |
4 | tristrane prizme | 8{3}
12{4} |
36 | 24 | O | D3 | |
UC31 | dro | ![]() |
8 | tristrane prizme | 16{3}
24{4} |
72 | 48 | Oh | D3 | |
UC32 | kri | ![]() |
10 | tristrane prizme | 20{3}
30{4} |
90 | 60 | I | D3 | |
UC33 | dri | ![]() |
20 | tristrane prizme | 40{3}
60{4} |
180 | 60 | 2 sestavna dela poliedra vpadata v vsako oglišče | Ih | D3 |
UC34 | kred | ![]() |
6 | petstrane prizme | 30{4}
12{5} |
90 | 60 | I | D5 | |
UC35 | dird | ![]() |
12 | petstrane prizme | 60{4}
24{5} |
180 | 60 | 2 sestavna dela poliedra vpadata v vsako oglišče | Ih | D5 |
UC36 | gikrid | ![]() |
6 | pentagramske prizme | 30{4}
12{5/2} |
90 | 60 | I | D5 | |
UC37 | giddird | ![]() |
12 | pentagramske prizme | 60{4}
24{5/2} |
180 | 60 | 2 sestavna dela poliedra vpadata v vsakem oglišču | Ih | D5 |
UC38 | griso | ![]() |
4 | šeststrane prizme | 24{4}
8{6} |
72 | 48 | Oh | D3d | |
UC39 | rosi | ![]() |
10 | šeststrane prizme | 60{4}
20{6} |
180 | 120 | Ih | D3d | |
UC40 | rassid | ![]() |
6 | desetstrane prizme | 60{4}
12{10} |
180 | 120 | Ih | D5d | |
UC41 | grassid | ![]() |
6 | dekagramske prizme | 60{4}
12{10/3} |
180 | 120 | Ih | D5d | |
UC42 | gassic | ![]() |
3 | kvadratne antiprizme | 24{3}
6{4} |
48 | 24 | O | D4 | |
UC43 | gidsac | ![]() |
6 | kvadratne antiprizme | 48{3}
12{4} |
96 | 48 | Oh | D4 | |
UC44 | sassid | ![]() |
6 | pentagramske antiprizme | 60{3}
12{5/2} |
120 | 60 | I | D5 | |
UC45 | sadsid | ![]() |
12 | pentagramske antiprizme | 120{3}
24{5/2} |
240 | 120 | Ih | D5 | |
UC46 | siddo | ![]() |
2 | ikozaedri | (16+24){3} | 60 | 24 | Oh | Th | |
UC47 | sne | ![]() |
5 | ikozaedri | (40+60){3} | 150 | 60 | Ih | Th | |
UC48 | presipsido | ![]() |
2 | veliki dodekaedri | 24{5} | 60 | 24 | Oh | Th | |
UC49 | presipsi | ![]() |
5 | veliki dodekaedri | 60{5} | 150 | 60 | Ih | Th | |
UC50 | passipsido | ![]() |
2 | mali stelirani dodekaedri | 24{5/2} | 60 | 24 | Oh | Th | |
UC51 | passipsi | ![]() |
5 | mali stelirani dodekaedri | 60{5/2} | 150 | 60 | Ih | Th | |
UC52 | sirsido | ![]() |
2 | veliki ikozaedri | (16+24){3} | 60 | 24 | Oh | Th | |
UC53 | sirsei | ![]() |
5 | veliki ikozaedri | (40+60){3} | 150 | 60 | Ih | Th | |
UC54 | tisso | ![]() |
2 | prisekan tetraedri | 8{3}
8{6} |
36 | 24 | Oh | Td | |
UC55 | taki | ![]() |
5 | prisekani tetraedri | 20{3}
20{6} |
90 | 60 | I | T | |
UC56 | te | ![]() |
10 | prisekani tetraedri | 40{3}
40{6} |
180 | 120 | Ih | T | |
UC57 | harie | ![]() |
5 | prisekane kocke | 40{3}
30{8} |
180 | 120 | Ih | Th | |
UC58 | quahri | ![]() |
5 | zvezdni prisekani heksaedri | 40{3}
30{8/3} |
180 | 120 | Ih | Th | |
UC59 | arie | ![]() |
5 | kubooktaedri | 40{3}
30{4} |
120 | 60 | Ih | Th | |
UC60 | gari | ![]() |
5 | kubohemioktaedri | 30{4}
20{6} |
120 | 60 | Ih | Th | |
UC61 | iddei | ![]() |
5 | oktahemioktaedri | 40{3}
20{6} |
120 | 60 | Ih | Th | |
UC62 | rasseri | ![]() |
5 | rombikubooktaedri | 40{3}
(30+60){4} |
240 | 120 | Ih | Th | |
UC63 | rasher | ![]() |
5 | mali rombihekaedri | 60{4}
30{8} |
240 | 120 | Ih | Th | |
UC64 | rahrie | ![]() |
5 | mali kubikubooktaedri | 40{3}
30{4} 30{8} |
240 | 120 | Ih | Th | |
UC65 | raquahri | ![]() |
5 | veliki kubikubooktaedri | 40{3}
30{4} 30{8/3} |
240 | 120 | Ih | Th | |
UC66 | rasquahr | ![]() |
5 | veliki rombiheksaedri | 60{4}
30{8/3} |
240 | 120 | Ih | Th | |
UC67 | rasquahpri | ![]() |
5 | nekonveksni veliki rombikubooktaedri | 40{3}
(30+60){4} |
240 | 120 | Ih | Th | |
UC68 | disco | ![]() |
2 | prirezane kocke | (16+48){3}
12{4} |
120 | 48 | Oh | O | |
UC69 | dissid | ![]() |
2 | prirezani dodekaedri | (40+120){3}
24{5} |
300 | 120 | Ih | I | |
UC70 | giddasid | ![]() |
2 | veliki prirezan ikozidodekaedri | (40+120){3}
24{5/2} |
300 | 120 | Ih | I | |
UC71 | gidsid | ![]() |
2 | veliki obrnjeni prirezani ikozidodekaedri | (40+120){3}
24{5/2} |
300 | 120 | Ih | I | |
UC72 | gidrissid | ![]() |
2 | veliki retroprirezan ikozidodekaedri | (40+120){3}
24{5/2} |
300 | 120 | Ih | I | |
UC73 | disdid | ![]() |
2 | prirezani dodekadodekaedri | 120{3}
24{5} 24{5/2} |
300 | 120 | Ih | I | |
UC74 | idisdid | ![]() |
2 | obrnjeni prirezani dodekadodekaedri | 120{3}
24{5} 24{5/2} |
300 | 120 | Ih | I | |
UC75 | desided | ![]() |
2 | prirezani ikozidodekadodekaedri | (40+120){3}
24{5} 24{5/2} |
360 | 120 | Ih | I |