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Hemi-octahedron

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by 4 triangles), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected and dividing the hemisphere into four equal parts. It can be seen as a
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It has an unexpected property that there are two distinct edges between every pair of vertices – any two vertices define a
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It can be represented symmetrically as a hexagonal or square
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It has 4 triangular faces, 6 edges, and 3 vertices. Its
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Abstract regular polyhedron with 4 triangular faces
46:but its sources remain unclear because it lacks 8: 97: 77:Learn how and when to remove this message 88: 7: 14: 253:, containing half the faces of a 299: 23: 1: 251:abstract regular polyhedron 110:abstract regular polyhedron 406: 348:Abstract Regular Polytopes 96: 271:It can be realized as a 32:This article includes a 61:more precise citations. 281:real projective plane 273:projective polyhedron 115:projective polyhedron 390:Projective polyhedra 170:Vertex configuration 331:Hemicube (geometry) 375:The hemioctahedron 288:without its base. 255:regular octahedron 34:list of references 321:Hemi-dodecahedron 239: 238: 87: 86: 79: 397: 364: 326:Hemi-icosahedron 303: 293:Schlegel diagram 212: 195: 188: 176: 164: 101: 89: 82: 75: 71: 68: 62: 57:this article by 48:inline citations 27: 26: 19: 405: 404: 400: 399: 398: 396: 395: 394: 380: 379: 371: 362: 344:McMullen, Peter 342: 339: 317: 262:dual polyhedron 247:hemi-octahedron 219:Dual polyhedron 210: 205: 194: 190: 186: 182:Schläfli symbol 174: 159: 112: 92:Hemi-octahedron 83: 72: 66: 63: 52: 38:related reading 28: 24: 17: 12: 11: 5: 403: 401: 393: 392: 382: 381: 378: 377: 370: 369:External links 367: 366: 365: 360: 338: 335: 334: 333: 328: 323: 316: 313: 305: 304: 286:square pyramid 237: 236: 234:non-orientable 231: 227: 226: 221: 215: 214: 208: 203: 201:Symmetry group 197: 196: 192: 184: 178: 177: 172: 166: 165: 157: 151: 150: 147: 141: 140: 137: 131: 130: 124: 118: 117: 107: 103: 102: 94: 93: 85: 84: 42:external links 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 402: 391: 388: 387: 385: 376: 373: 372: 368: 363: 361:0-521-81496-0 357: 353: 349: 345: 341: 340: 336: 332: 329: 327: 324: 322: 319: 318: 314: 312: 310: 302: 298: 297: 296: 294: 289: 287: 282: 278: 274: 269: 267: 263: 258: 256: 252: 248: 244: 235: 232: 228: 225: 222: 220: 216: 211: 204: 202: 198: 185: 183: 179: 173: 171: 167: 162: 158: 156: 152: 148: 146: 142: 138: 136: 132: 129: 125: 123: 119: 116: 111: 108: 104: 100: 95: 90: 81: 78: 70: 67:November 2014 60: 56: 50: 49: 43: 39: 35: 30: 21: 20: 347: 306: 290: 277:tessellation 270: 259: 246: 240: 160: 73: 64: 53:Please help 45: 155:Euler char. 59:introducing 337:References 230:Properties 213:, order 24 128:triangles 113:globally 384:Category 315:See also 266:hemicube 243:geometry 224:hemicube 145:Vertices 352:162–165 279:of the 264:is the 187:{3,4}/2 175:3.3.3.3 55:improve 358:  249:is an 309:digon 191:{3,4} 135:Edges 122:Faces 40:, or 356:ISBN 245:, a 106:Type 275:(a 241:In 189:or 163:= 1 386:: 354:, 311:. 295:: 268:. 257:. 126:4 44:, 36:, 209:4 207:S 193:3 161:χ 149:3 139:6 80:) 74:( 69:) 65:( 51:.

Index

list of references
related reading
external links
inline citations
improve
introducing
Learn how and when to remove this message

abstract regular polyhedron
projective polyhedron
Faces
triangles
Edges
Vertices
Euler char.
Vertex configuration
Schläfli symbol
Symmetry group
S4
Dual polyhedron
hemicube
non-orientable
geometry
abstract regular polyhedron
regular octahedron
dual polyhedron
hemicube
projective polyhedron
tessellation
real projective plane

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