Uniform polytera

This page covers flag graphs for the uniform polytera, 5-dimensional polytopes.

This page will proceed in the same order as the Bowers list of polytera. In this page, rank-3 edges will be colored green and rank-4 edges will be colored blue.

Table of contents

Category 1: Primary Polytera

[Hedrondude]

They are primary.

A regular polyteron
16-hemi-10 ("Hehad") #4
5-choric hemiantiprism ("Phap") #5
Spino-5-choric hemiantiprism ("Nophap") #6
Demipenteract ("Hin") #7
Dis-16-teron ("Dah") #8
16-10 ("Han") #9
Retrodis-16 ("Radah") #10
Retropenteracti-16 ("Rinah") #11
16-teron ("Hit") #12

Category 2: Truncates

[Hedrondude]

The members of this category are the truncates or bitruncates of the members of the previous category. As such, their reduced flag graphs match each other in similar ways.

A truncated regular polyteron
Truncated 16-hemi-10 ("Thehid") #16
Truncated demipenteract ("Thin") #18
Truncated dis-16 ("Tadah") #19
Truncated 16-10 ("Tohan") #20
A bitruncated regular polyteron
Bitruncated 16-hemi-10 ("Bathehad") #24

Category 3: Rectates

[Hedrondude]

This category contains three regiments. Here is the rectified 6-teron regiment.

Rectified 6-teron ("Rix") #25
Cellibiprismatointercepted 6-teron ("Cabnix") #26
Faceted rectified 6-teron ("Firx") #27
Celli-6 ("Cax") #28
Biprismatodis-6 ("Baddix") #29
Cellintercepted dis-6 ("Cindax") #30
Spinobiprismato-6 ("Nobax") #31

The other regiment.

12-teron ("Dot") #32
Biprismato-12 ("Bad") #33
Biprismatointercepted 12-teron ("Bend") #34
Cellibiprismato-6 ("Cabbix") #35
Cellidis-6 ("Caddix") #36

The first seven members of the rectified penteract regiment have the same flag diagrams as corresponding members of the rectified 6-teron regiment. The other four are shown below.

10-triacontadi-16 ("Nath") #44
10-dis-16 ("Nadoh") #45
10-16 ("Nah") #46
10-32-dis-16 ("Natdoh") #47

Category 4: Rectified 32-teron Regiment

[Hedrondude]

This category is one regiment.

Rectified 32-teron ("Rat") #48
Retro-10-hemi-32 ("Rinhit") #54
32-hemi-32 ("Thit") #49
Retro-32-hemi-32 ("Rithit") #50
Octary 10-32-hemi-32 ("Onthet") #51
Octary 32-10-hemi-32 ("Othahit")
Inverti-32-hemi-32 ("Ithit") #53
Celli-32-hemi-32 ("Cathit") #55
Retro-32-celli-hemi-32 ("Ratchet") #59
Biprismato-32-hemi-32 ("Bathit") #56
Retro-32-biprismato-hemi-32 ("Ratobaht") #60
Celli-10-32 ("Cant") #57
Celli-10-hemi-32 ("Conhit") #63
Biprismato-10-32 ("Bant") #58
Biprismato-10-hemi-32 ("Bonhit") #64
Celli-32 ("Cat") #61
Celli-hemi-32 ("Chet") #65
Biprismato-32 ("Bat") #62
Biprismato-hemi-32 ("Boht") #66
Rectified 16-hemi-10 ("Rhohid") #67
Biprismato-10-dis-16-hemi-10 ("Bendhehad") #68
10-biprismatodis-16-hemi-10 ("Nabadhehad") #69
10-tris-16-hemi-10 ("Nathehid") #70
10-dis-16-hemi-10 ("Nedhehad") #71
Biprismato-10-tris-16-hemi-10 ("Benthahid") #72
Tris-16-10-hemi-10 ("Thinhed") #73
16-10-16-hemi-10 ("Hinhohid") #74
10-tris-16 ("Noth") #81
Dis-16-biprismato-10-hemi-10 ("Dohbinhed") #75
10-biprismato-tris-16-hemi-10 ("Nabthehid") #76
10-dis-16-hemi-10 ("Didhehad") #77
10-dis-16-biprismato-hemi-10 ("Nadahobhid") #78
Biprismato-10-tris-16 ("Banth") #91
10-tris-16-hemi-10 ("Dathehid") #79
16-16 ("Hah") #80
16-10-16 ("Hanoh") #82
Tris-16 ("Tuh") #83
Celli-10-dis-16 ("Candoh") #84
Biprismato-10-dis-16 ("Bandoh") #85
Cellitris-16 ("Cath") #86
Biprismatotris-16 ("Bath") #87
Cellidis-16 ("Cadoh") #88
Biprismatodis-16 ("Badoh") #89
Celli-10-tris-16 ("Canth") #90

Category 6: Sphenoverts

[Hedrondude]

This category contains three regiments of 15 polytera. Corresponding polytera in these regiments have the same reduced flag graph, so the captions will only specify those from the small rhombated 6-teron ("sarx") regiment.

Small rhombated 6-teron ("Sarx") #241
Retrosphenary 6-teron ("Rawx") #242
Lepidosphenary 6-teron ("Lawx") #243
Facetosphenary 6-teron ("Fawx") #244
Lepidosphenary biprismato-6 ("Lawbix") #245
Sphenary 6-teron ("Wax") #246
Retrosphenary celli-6 ("Rawcax") #247
Quasisphenary celli-6 ("Qwacox") #248
Quasisphenary biprismato-6 ("Qwabix") #249
Spinosphenary biprismato-6 ("Nawbix") #250
Spinosphenary celli-6 ("Newcax") #251
Invertisphenary 6-teron ("Iwax") #252
Thyridosphenary 6-teron ("Yawx") #254
Invertisphenary biprismato-6 ("Iwebix") #253
Thyridosphenary celli-6 ("Yawcax") #255

The other regiment in this category has 92 members. It has not been started yet.

Category 9: Podiumverts

[Hedrondude]

This category is composed of regiments of 15 polytera. Corresponding polytera (by geometry or by conjugation) in the regiments have the same reduced flag graph, so the captions will only specify those from the small cellated 10-16 ("scant") regiment.

Small cellated 10-32 ("Scant") #692
Small 32-biprismatodis-10 ("Satbadan") #693
Small cellitesseracti-10 ("Scotan") #694
Small celli-32-dis-10 ("Sactadan") #695
Small cellidis-10-32 ("Scadant") #696
Small biprismatocelli-10 ("Sobcan") #697
Small cellibiprismato-10 ("Scabbin") #698
Small 10-10-32 ("Sinnont") #699
Small biprismatodiscelli-10 ("Sabdacan") #700
Small biprismato-10 ("Sobin") #701
Small 32-cellidis-10 ("Stacdan") #702
Small celli-10 ("Scan") #703
Small tesseracti-10 ("Stan") #704
Small cellibiprismato-32-dis-10 ("Scabtadin") #705
Small cellibiprismatodis-10-32 ("Sacbadant") #706

The small cellated 12-teron ("scad") regiment has some members with double symmetry.

Small cellated 12-teron ("Scad") #681
12-biprismatohemi-12 ("Dibhid") #682
Cellated hemi-12 ("Chad") #683
12-hemi-12 ("Dehad") #686
Biprismatocellihemi-12 ("Bachid") #687
Biprismatohemi-12 ("Behad") #688
12-cellihemi-12 ("Dachid") #689

Category 10: Greater Truncates

[Hedrondude]

This category contains some of the most intricate diagrams. It is incomplete.

Great rhombate
Great rhombated 16-hemi-16 ("Grahehad") #725
Great birhombate
Great birhombate with doubled symmetry:
Great birhombated 12-teron ("Gibrid") #729

Category 13: Prismatorhombates and Kin

[Hedrondude]

The first part of this category contains five regiments of three polytera each. The first two members of each regiment have the same reduced flag diagram, and the third one is different. It is incomplete.

The first two members of the regiment

The rest of the category has not been started yet.

Category 19: Miscellaneous

[Hedrondude]

This category is not yet complete.

Small ditetrahedrary 600-120-choron antiprism ("Sidtaxhiap") #1288
Grand ditetrahedrary 600-120-choron antiprism ("Gadtaxhiap") #1289
Hollostelli-24-choron antiprism ("Hosiap") #1290
Inverted hollow stellated 24-choric antiprism ("Ihsiap") #1291
Hollow stellated 24-choric retroantiprism ("Hesirap") #1292
Retrohollow stellated 24-choric antiprism ("Rahsiap") #1295
Spinohollow stellated 24-choric hemiantiprism ("Nahsihap") #1296
Hollow stellated 24-choric hemiantiprism ("Hesihap") #1297
Dodecahedronary prismato-600-choric alterprism ("Dopixa") #1293
Invertidodecahedronary 120-choric alterprism ("Idhia") #1294